diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 81ea4f054..b77742ce7 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -25,23 +25,17 @@ jobs:
     if: ${{ github.repository_owner == 'pypa' || github.event_name != 'schedule' }}
     runs-on: ubuntu-latest
     timeout-minutes: 20
-    continue-on-error: >-
-      ${{ fromJSON(matrix.continue-on-error) }}
     strategy:
       matrix:
         noxenv:
         - build
-        continue-on-error:
-        - false
-        include:
-        - noxenv: linkcheck
-          continue-on-error: >-  # Don't block PRs on linkcheck unrelated failures
-            ${{ toJSON(github.event_name == 'pull_request') }}
+        - linkcheck
 
     steps:
       - uses: actions/checkout@08c6903cd8c0fde910a37f88322edcfb5dd907a8 # v5.0.0
         with:
           persist-credentials: false
+          fetch-depth: 0  # needed to compare PR links against the base commit
 
       - name: Set up Python
         uses: actions/setup-python@e797f83bcb11b83ae66e0230d6156d7c80228e7c # v6.0.0
@@ -55,12 +49,22 @@ jobs:
           python -m pip install --upgrade nox virtualenv
 
       - name: Nox ${{ matrix.noxenv }}
+        continue-on-error: >-
+          ${{ matrix.noxenv == 'linkcheck' && github.event_name == 'pull_request' }}
         env:
           # Authenticate github.com requests during linkcheck to avoid rate limits.
           GITHUB_TOKEN: ${{ matrix.noxenv == 'linkcheck' && github.token || '' }}
         run: |
           python -m nox -s ${{ matrix.noxenv }}
 
+      - name: Check links introduced by the PR
+        if: >-
+          ${{ always() && matrix.noxenv == 'linkcheck' && github.event_name == 'pull_request' }}
+        env:
+          BASE_SHA: ${{ github.event.pull_request.base.sha }}
+        run: |
+          python scripts/check_new_link_failures.py --base "$BASE_SHA" --report build/output.json
+
 
   check:
     # This job does nothing and is only used for the branch protection
diff --git a/scripts/check_new_link_failures.py b/scripts/check_new_link_failures.py
new file mode 100644
index 000000000..5e7373707
--- /dev/null
+++ b/scripts/check_new_link_failures.py
@@ -0,0 +1,85 @@
+"""Fail when Sphinx reports a URL added by the current PR as broken."""
+
+from __future__ import annotations
+
+import argparse
+import json
+import re
+import subprocess
+from pathlib import Path
+
+URL_RE = re.compile(r"https?://[^\s<>()\[\]{}\"']+")
+TRAILING_PUNCTUATION = ".,;:!?`"
+
+
+def _added_urls(base: str) -> set[str]:
+    result = subprocess.run(
+        [
+            "git",
+            "diff",
+            "--unified=0",
+            "--diff-filter=AM",
+            f"{base}...HEAD",
+            "--",
+            "source",
+        ],
+        check=True,
+        capture_output=True,
+        text=True,
+    )
+    urls: set[str] = set()
+    for line in result.stdout.splitlines():
+        if not line.startswith("+") or line.startswith("+++"):
+            continue
+        for match in URL_RE.findall(line[1:]):
+            urls.add(match.rstrip(TRAILING_PUNCTUATION))
+    return urls
+
+
+def _broken_urls(report: Path) -> dict[str, str]:
+    if not report.is_file():
+        raise SystemExit(f"linkcheck report not found: {report}")
+
+    broken: dict[str, str] = {}
+    for number, raw_line in enumerate(
+        report.read_text(encoding="utf-8").splitlines(), 1
+    ):
+        if not raw_line.strip():
+            continue
+        try:
+            record = json.loads(raw_line)
+        except json.JSONDecodeError as exc:
+            raise SystemExit(f"invalid JSON in {report} line {number}: {exc}") from exc
+        if record.get("status") != "broken":
+            continue
+        uri = record.get("uri")
+        if isinstance(uri, str):
+            broken[uri] = str(record.get("info") or "broken")
+    return broken
+
+
+def main() -> int:
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--base", required=True, help="PR base commit SHA")
+    parser.add_argument("--report", type=Path, default=Path("build/output.json"))
+    args = parser.parse_args()
+
+    added = _added_urls(args.base)
+    if not added:
+        print("No newly added HTTP(S) links found in source/. ")
+        return 0
+
+    broken = _broken_urls(args.report)
+    failures = {url: broken[url] for url in sorted(added & broken.keys())}
+    if not failures:
+        print(f"All {len(added)} newly added HTTP(S) link(s) passed Sphinx linkcheck.")
+        return 0
+
+    print("Broken links introduced by this PR:")
+    for url, info in failures.items():
+        print(f"- {url}: {info}")
+    return 1
+
+
+if __name__ == "__main__":
+    raise SystemExit(main())