Accies conceded a sixth-minute opener when Christian Nade latched onto Bruno Aguiar's head-flick and, despite looking suspiciously offside, slid the ball under Tomas Cerny, as Martin Canning and Mark McLaughlin challenged.
If the goal was indeed offside, that would be the third in four games against Billy Reid's First Division champions.
While the goal looked to be slightly harsh against Hamilton, Hearts went on to dominate the remainder of the first half, with Nade in particular looking to be in the mood.
In the 27th minute the striker, with his back to goal, hooked a shot inches past the left post, despite the attentions of McLaughlin.
Three minutes later David Obua found Nade on the right. His swerving shot from distance was beaten out by Cerny, Simon Mensing fluffed his clearance attempt and the ball fell back to Nade, but this time his effort was saved.
Hamilton's best chance fell to David Graham who drove in from the left by-line, but Janos Balogh blocked his near-post 38th-minute effort.
The addition of Richard Offiong for Lucas Akins at the interval breathed new life into Hamilton and they dominated the second period.
First, however, Cerny was forced into decent saves to deny Aguiar and Andy Driver.
Aguiar's cross from the right was then blazed over by Nade at full stretch. The striker seemed to aggravate a hamstring in the process and had to be replaced by Jamie Mole.
Hamilton rallied after that and Mensing's cross from the right was well met by Offiong, but his header was saved at the far post.
Accies had one final chance after 72 minutes when Graham's inviting cross from the right was headed over by James McArthur, but Hearts held on for the win and Accies' winless streak continues.
The Lanarkshire side don't seem to have too many problems, but a lack of firepower up front is ultimately costing them, and they remain rooted to the bottom of the SPL table.