diff --git a/src/pydata_sphinx_theme/assets/scripts/pydata-sphinx-theme.js b/src/pydata_sphinx_theme/assets/scripts/pydata-sphinx-theme.js
index f2b677077..48a1e4257 100644
--- a/src/pydata_sphinx_theme/assets/scripts/pydata-sphinx-theme.js
+++ b/src/pydata_sphinx_theme/assets/scripts/pydata-sphinx-theme.js
@@ -194,7 +194,7 @@ var findSearchInput = () => {
     } else {
       // must be at least one persistent form, use the first persistent one
       form = document.querySelector(
-        "div:not(.search-button__search-container) > form.bd-search",
+        ":not(#pst-search-dialog) > form.bd-search",
       );
     }
     return form.querySelector("input");
@@ -208,22 +208,30 @@ var findSearchInput = () => {
  */
 var toggleSearchField = () => {
   // Find the search input to highlight
-  let input = findSearchInput();
+  const input = findSearchInput();
 
   // if the input field is the hidden one (the one associated with the
   // search button) then toggle the button state (to show/hide the field)
-  let searchPopupWrapper = document.querySelector(".search-button__wrapper");
-  let hiddenInput = searchPopupWrapper.querySelector("input");
+  const searchDialog = document.getElementById("pst-search-dialog");
+  const hiddenInput = searchDialog.querySelector("input");
   if (input === hiddenInput) {
-    searchPopupWrapper.classList.toggle("show");
-  }
-  // when toggling off the search field, remove its focus
-  if (document.activeElement === input) {
-    input.blur();
+    if (searchDialog.open) {
+      searchDialog.close();
+    } else {
+      // Note: browsers should focus the input field inside the modal dialog
+      // automatically when it is opened.
+      searchDialog.showModal();
+    }
   } else {
-    input.focus();
-    input.select();
-    input.scrollIntoView({ block: "center" });
+    // if the input field is not the hidden one, then toggle its focus state
+
+    if (document.activeElement === input) {
+      input.blur();
+    } else {
+      input.focus();
+      input.select();
+      input.scrollIntoView({ block: "center" });
+    }
   }
 };
 
@@ -295,11 +303,30 @@ var setupSearchButtons = () => {
     btn.onclick = toggleSearchField;
   });
 
-  // Add the search button overlay event callback
-  let overlay = document.querySelector(".search-button__overlay");
-  if (overlay) {
-    overlay.onclick = toggleSearchField;
-  }
+  // If user clicks outside the search modal dialog, then close it.
+  const searchDialog = document.getElementById("pst-search-dialog");
+  // Dialog click handler includes clicks on dialog ::backdrop.
+  searchDialog.addEventListener("click", (event) => {
+    if (!searchDialog.open) {
+      return;
+    }
+
+    // Dialog.getBoundingClientRect() does not include ::backdrop. (This is the
+    // trick that allows us to determine if click was inside or outside of the
+    // dialog: click handler includes backdrop, getBoundingClientRect does not.)
+    const { left, right, top, bottom } = searchDialog.getBoundingClientRect();
+
+    // 0, 0 means top left
+    const clickWasOutsideDialog =
+      event.clientX < left ||
+      right < event.clientX ||
+      event.clientY < top ||
+      bottom < event.clientY;
+
+    if (clickWasOutsideDialog) {
+      searchDialog.close();
+    }
+  });
 };
 
 /*******************************************************************************
diff --git a/src/pydata_sphinx_theme/assets/styles/components/_search.scss b/src/pydata_sphinx_theme/assets/styles/components/_search.scss
index ce8256d4c..e75b08d72 100644
--- a/src/pydata_sphinx_theme/assets/styles/components/_search.scss
+++ b/src/pydata_sphinx_theme/assets/styles/components/_search.scss
@@ -16,6 +16,15 @@
     color: var(--pst-color-text-muted);
   }
 
+  // Hoist the focus ring from the input field to its parent
+  &:focus-within {
+    box-shadow: $focus-ring-box-shadow;
+
+    input:focus {
+      box-shadow: none;
+    }
+  }
+
   .icon {
     position: absolute;
     color: var(--pst-color-border);
@@ -28,7 +37,11 @@
     color: var(--pst-color-text-muted);
   }
 
-  input {
+  input.form-control {
+    background-color: var(--pst-color-background);
+    color: var(--pst-color-text-base);
+    border: none;
+
     // Inner-text of the search bar
     &::placeholder {
       color: var(--pst-color-text-muted);
@@ -39,46 +52,36 @@
     &::-webkit-search-decoration {
       appearance: none;
     }
+
+    &:focus,
+    &:focus-visible {
+      color: var(--pst-color-text-muted);
+    }
   }
 
   // Shows off the keyboard shortcuts for the button
   .search-button__kbd-shortcut {
     display: flex;
-    position: absolute;
-    right: 0.5rem;
+    margin-inline-end: 0.5rem;
     color: var(--pst-color-border);
   }
 }
 
-.form-control {
-  background-color: var(--pst-color-background);
-  color: var(--pst-color-text-base);
-
-  &:focus,
-  &:focus-visible {
-    border: none;
-    background-color: var(--pst-color-background);
-    color: var(--pst-color-text-muted);
-  }
-}
-
 /**
  * Search button - located in the navbar
  */
-
-// Search link icon should be a bit bigger since it is separate from icon links
 .search-button i {
+  // Search link icon should be a bit bigger since it is separate from icon links
   font-size: 1.3rem;
 }
 
-// __search-container will only show up when we use the search pop-up bar
-.search-button__search-container,
-.search-button__overlay {
+/**
+ * The search modal <dialog>
+ */
+#pst-search-dialog {
   display: none;
-}
 
-.search-button__wrapper.show {
-  .search-button__search-container {
+  &[open] {
     display: flex;
 
     // Center in middle of screen just underneath header
@@ -91,30 +94,24 @@
     margin-top: 0.5rem;
     width: 90%;
     max-width: 800px;
-  }
+    background-color: transparent;
+    padding: $focus-ring-width;
+    border: none;
 
-  .search-button__overlay {
-    display: flex;
-    position: fixed;
-    z-index: $zindex-modal-backdrop;
-    background-color: black;
-    opacity: 0.5;
-    width: 100%;
-    height: 100%;
-    top: 0;
-    left: 0;
-  }
+    &::backdrop {
+      background-color: black;
+      opacity: 0.5;
+    }
 
-  form.bd-search {
-    flex-grow: 1;
-    padding-top: 0;
-    padding-bottom: 0;
-  }
+    form.bd-search {
+      flex-grow: 1;
 
-  // Font and input text a bit bigger
-  svg,
-  input {
-    font-size: var(--pst-font-size-icon);
+      // Font and input text a bit bigger
+      svg,
+      input {
+        font-size: var(--pst-font-size-icon);
+      }
+    }
   }
 }
 
@@ -141,7 +138,7 @@
     border-radius: $search-button-border-radius;
   }
 
-  // The keyboard shotcut text
+  // The keyboard shortcut text
   .search-button__default-text {
     font-size: var(--bs-nav-link-font-size);
     font-weight: var(--bs-nav-link-font-weight);
diff --git a/src/pydata_sphinx_theme/theme/pydata_sphinx_theme/components/search-field.html b/src/pydata_sphinx_theme/theme/pydata_sphinx_theme/components/search-field.html
index c1d605292..cd6891028 100644
--- a/src/pydata_sphinx_theme/theme/pydata_sphinx_theme/components/search-field.html
+++ b/src/pydata_sphinx_theme/theme/pydata_sphinx_theme/components/search-field.html
@@ -6,7 +6,6 @@
   <input type="search"
          class="form-control"
          name="q"
-         id="search-input"
          placeholder="{{ theme_search_bar_text }}"
          aria-label="{{ theme_search_bar_text }}"
          autocomplete="off"
diff --git a/src/pydata_sphinx_theme/theme/pydata_sphinx_theme/layout.html b/src/pydata_sphinx_theme/theme/pydata_sphinx_theme/layout.html
index 9fb914b50..496dfc096 100644
--- a/src/pydata_sphinx_theme/theme/pydata_sphinx_theme/layout.html
+++ b/src/pydata_sphinx_theme/theme/pydata_sphinx_theme/layout.html
@@ -63,10 +63,9 @@
           id="pst-secondary-sidebar-checkbox"/>
   <label class="overlay overlay-secondary" for="pst-secondary-sidebar-checkbox"></label>
   {# A search field pop-up that will only show when the search button is clicked #}
-  <div class="search-button__wrapper">
-    <div class="search-button__overlay"></div>
-    <div class="search-button__search-container">{% include "../components/search-field.html" %}</div>
-  </div>
+  <dialog id="pst-search-dialog">
+    {% include "../components/search-field.html" %}
+  </dialog>
 
   {% include "sections/announcement.html" %}