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.
Hamilton went into the game on a run of six games unbeaten in all competitions - and five wins in that sequence - but Hearts are competing for Europa League qualification from the Premiership and just had too much quality throughout.
Hearts dominated the first half but without doing too much with it. They had plenty of possession and when the opener came it wasn't really a surprise, but they didn't have too many clear-cut chances.
Hamilton improved considerably in the second half, with Matty Shiels pushed up front, and forced a couple of decent saves, but still not enough to cause considerable concern.
Josh Ginnelly did a lot of the running for the visitors, and Humphrys had a couple of chances he should have done better with before opening the scoring.
James Hill should have added a second before the interval from Stephen Kingsley's cross following a short corner move.
But tenacity from Devlin saw him force his way past Dan O'Reilly in the box and he stabbed a low shot into the right corner to end the game as a contest.
Accies head coach John Rankin made two change to the side that beat Queen of the South 2-1 in the SPFL Trust Trophy semi-finals on Tuesday. Goalkeeper Ryan Fulton came in for Jamie Smith, while Reghan Tumilty replaced Dario Zanatta.
His Hearts counterpart Robbie Neilson made four changes to the side that won 3-1 against Dundee United last weekend. Jorge Grant, Alex Cochrane, Michael Smith and Stephen Humphrys came in for Kyle Rowles, Alan Forrest, Andy Halliday and suspended Lawrence Shankland.
Hearts started well, with Barrie McKay and Humphrys combining inside the box, but the ball landed past the right post in the opening minute.
Hill got his head onto a Robert Snodgrass corner from the right in three minutes, but it was no problem for Ryan Fulton.
McKay's corner from the left was headed over by Stephen Kingsley in 16 minutes.
Humphrys had a good chance when he was picked out unmarked at the back post at McKay's corner from the left in 23 minutes, but fired over.
Kingsley's cross from the left was headed by Humphrys in 28 minutes, but it was a comfortable save when the Hearts man should have done better.
But when Josh Ginnelly fed Humphrys moments later he blasted across Fulton and into the bottom right corner.
Hamilton had a rare foray up front when Lucas De Bolle picked out Jean-Pierre Tiehi on the edge of the box, but his shot on the turn flew high and wide in 36 minutes.
Hearts went close to doubling their lead in 41 minutes when from a short corner on the right Kingley slipped an angled shot towards the left corner, with Hill just unable to connect with a tap-in.
Hamilton came back into the game in the second half and in 64 minutes Matty Shiels had a low drive well saved by Zander Clark from just outside the box.
At the other end Snodgrass' powerful shot was well held by Fulton in 66 minutes.
De Bolle had a low shot saved in 68 minutes as Hamilton continued to threaten.
But Hearts grabbed their second goal in 79 minutes when Devlin forced the ball home.
Sub Alan Forrest went close to adding a third in the last minute of the 90, but Fulton held his rising shot well.
HAMILTON: Fulton, Tumilty (Zanatta, 70), Owens (Winter, 70), McGowan, Reilly, Shiels, Martin, Stephenson (McGinn, 54), De Bolle, L. Smith (One, 61), Tiehi.
Subs (not used): J. Smith (GK), Easton, Newbury.
Booked: Tumilty (13). Martin (45+1)
HEARTS: Clark, Hill, Sibbick, Cochrane, Smith (Atkinson 73), Snodgrass, Grant (Forrest, 58), Kingsley, Humphrys (Devlin, 65), McKay (Oda, 73), Ginnelly.
Subs (not used): Stewart (GK), Kiomourtzoglou, Rowles, Halliday, Kuol.
Referee: Kevin Clancy.
Attendance: 4731.
Follow Lanarkshire Live Sport on Twitter via @LanLiveSport, like us on Facebook or find us on Instagram for the latest sports news, pictures and video.
