Arnaud Djoum, Esmael Goncalves, Jamie Walker and Malaury Martin struck the goals at Tynecastle to give the home side their first win in six matches.
Hamilton have won just once in Gorgie since World War II, and that was 40 years ago. They never looked likely to make history on what was a dismal afternoon for the Lanarkshire club.
That said, Hearts' performance was vastly improved following several poor results including three straight defeats in their last three outings. Had it not been for some outstanding first-half saves from the Hamilton goalkeeper Gary Woods, this would have been a trouncing of epic proportions.
Goncalves returned to Hearts' starting line-up after suspension, while Walker was back after a head knock. The Edinburgh side were out to banish a frustrating run of five games without a win against the Ladbrokes Premiership's second bottom club. They dominated the first half and fashioned four decent openings inside the opening ten minutes.
Walker's back-post header forced Woods into an early save. Goncalves then found himself through on goal when Scott McMann missed attempting to clear Alex Tziolis' forward ball - but the Portuguese was thwarted by another excellent block from the diving Woods.
The visiting keeper then pushed Sam Nicholson's left-footed drive for a corner. Finally, an excellent spring to his right saw Woods push Goncalves' header from Lennard Sowah's cross to safety. Hearts were entitled to wonder why they weren't ahead while Woods was enjoying the game of his life.
The hosts were still wondering on 29 minutes when Tziolis beautifully volleyed Walker's corner at goal first time from the edge of the penalty box. Again, Woods was equal to the task. Walker tried an attempt from similar distance minutes later but Hamilton, once more, were indebted to their goalkeeper for pushing the effort clear.
Hearts were playing some terrific football but somehow hadn't scored as the interval approached. Seconds from the whistle, they eventually forced a breakthrough. Andraz Struna's intelligent through pass found Sam Nicholson for a low cross which was cleared. Tziolis tried a follow up shot which was blocked, and Djoum dispatched the rebound high into the net.
The home support's relief at the breakthrough would have become joy at a second Hearts goal just after half-time. However, Goncalves' finish was disallowed due to an offside flag. The striker didn't need to wait long for his first goal in Gorgie. When Woods mistakenly picked up a backpass thinking the referee had blown for a foul, Hearts were awarded an indirect free-kick inside the opposition box. Cowie touched it for Goncalves to blast high into the rigging.
Hamilton were dead and buried three minutes later. Another free-kick saw Walker step up from almost 25 yards to curl a perfect strike high into Woods' top right corner. It was no more than the hosts deserved at that point and they played out the final half hour of the afternoon in relative comfort.
Substitute Martin claimed the fourth goal two minutes from the end with a well-executed free-kick low past Woods. That completed the scoring as Hearts returned to winning ways.
Hearts (4-4-2): Hamilton; Struna, Avlonitis, Nowak, Sowah; Cowie, Tziolis, Djoum; Nicholson, Goncalves, Walker.
63: Martin for Djoum
69: Choulay for Nicholson
80: Johnsen for Walker
Unused subs: Noring, Kitchen, Buaben, Smith.
Hamilton (3-4-1-2): Woods; Sarris Donati McMann; Skondras Docherty Redmond Imrie; Crawford; Bingham Brophy.
56: Gogic for Imrie
65: Gillespie for Brophy
74: Tierney for Bingham
Unused subs: Matthews, Kurtaj, Watson, Boyd.
Referee: Craig Thomson.