Goals from Marius Zaliukas and Andrew Driver secured the three points and ensured there would be no lingering fallout from Wednesday's epic second-round cup tie against Airdrie.
Accies did hit back through substitute Derek Lyle late on but it was not enough to prevent them slumping to their second successive top-flight reverse following last week's defeat at Kilmarnock.
Both teams had a point to prove in this clash at New Douglas Park.
Hamilton were keen to return to winning ways in the SPL and demonstrate their ability to cope with the pressures of the top flight, while Hearts knew they had to bounce back from that shock cup defeat.
Accies boss Billy Reid made three changes from the side who progressed in the League Cup in midweek.
Skipper Alex Neil and Richard Offiong both returned from injury and Joel Thomas was drafted into the starting line-up after grabbing a goal against Clyde.
Accies signed three players on Friday - Stephen Ettien, Michael Videira and Chris Casement - although only Casement made the 18-man squad.
Hearts made just one change from the side who crashed out of the cup, with Driver replacing Saulius Mikoliunas.
Chances were few and far between early on, although the visitors started slightly better, with David Obua and Driver both firing over after trying their luck from distance.
At the other end, Lucas Akins whipped an inviting ball into the box which was smothered by goalkeeper Marian Kello, with Thomas lurking in the goalmouth.
The breakthrough came after 18 minutes when Hearts opened the scoring. Driver's corner was met by the head of Zaliukas, who took advantage of poor defending to nod home from close range.
Accies made their first change a minute later when the injured Chris Swailes was withdrawn for James McCarthy.
Hamilton tried to hit back and Offiong supplied a decent angled pass to McCarthy but he was denied the sight of the net bulging when Kello managed to block with his feet.
Elebert then came close with a free header which he nodded over as the home side pushed for a leveller before the interval.
Instead, it was Hearts who should have added to their lead. Laryea Kingston released Jamie Mole through on goal but his effort was well off target.
Goalkeeper Tomas Cerny then came to the rescue when he pulled off a great save after Obua had been set up by Michael Stewart.
Hamilton appealed for a penalty within a few minutes of the restart when McCarthy went to ground just inside the box under pressure from Christos Karipidis, but referee Craig Thomson ignored the pleas.
Stevenson then set up Akins for a header but he nodded over from eight yards, with Kello untroubled in the Hearts goal.
The home side's hopes of a comeback were dealt a blow when Hearts doubled Hearts' lead after 58 minutes.
Elebert attempted to play a pass to Simon Mensing but he lost control of the ball and allowed Driver to sweep in and slot past Cerny from close range.
Hamilton refused to give up and gave themselves hope of snatching a point when they pulled a goal back with 11 minutes to go.
A superb long cross from James McArthur found substitute Derek Lyle, who left Kello with no chance with a glancing header from 10 yards.
Kingston could have killed off the hosts when he pounced on a rebound, after his free-kick had been blocked, only to see his shot fizz across the face of goal and wide of the upright.
Offiong then vainly appealed for a penalty late on but again the home side failed with their claims and Hearts returned to Edinburgh with maximum points.