Hamilton crashed out of the Scottish Cup fifth round as Stephen Humphrys and Cammy Devlin earned Hearts a comfortable passage to the last 16.
On-loan Wigan star Humphrys struck his second goal in as many games just before the half-hour, and substitute Devlin scrambled in a second with 11 minutes left to see the Edinburgh giants progress.
Hearts dominated the first half, and Hamilton did better in the second half but still couldn't test Zander Clark enough in the visitors' goal.
