This isn't via API, but on GitHub.com: if you have the latest commit SHA and the commit count, you can build the URL to find it:
https://github.com/USER/REPO/commits?after=LAST_COMMIT_SHA+COMMIT_COUNT_MINUS_2# Example. Commit count in this case was 1573https://github.com/sindresorhus/refined-github/commits/master ?after=a76ed868a84cd0078d8423999faaba7380b0df1b+1571