Martin Canning’s visitors notched their first win in eight league games despite losing influential midfielder Massimo Donati with 15 minutes remaining of this Tayside affair.
Ioannis Skondras gave Accies a 39th-minute lead before David Templeton made it 2-0 on 64 minutes, only for A-Jay Leitch-Smith’s 67th-minute penalty to give Neil McCann’s men some hope of a comeback.
Donati was then dismissed but substitute Antonio Raul Rojano killed the game off with a simple tap-in to pile more misery on the Dark Blues.
Dundee made four changes from the side which went down 1-0 to Betfred Cup finalists Motherwell in midweek.
Paul McGowan was installed as captain while Leitch-Smitch, Randy Wolters and Kerr Waddell all started as skipper Darren O’Dea, Kevin Holt, Sofien Moussa and Roarie Deacon all dropped out.
The visitors began brightly enough with former Rangers and Hearts winger Templeton seeing his early shot deflected wide for a corner.
Dundee could not find any real rhythm, although Wolters did try his luck just after the half-hour mark and saw his shot from a raking run go narrowly past Gary Woods’ near post.
But Hamilton took the lead in simple fashion in the 39th minute.
Dougie Imrie’s whipped cross eluded the entire home defence as Skondras arrived on a late run and the 27-year-old Greek right-back planted a header across Scott Bain.
Dundee tried to lift the pace after the break and Waddell had a shot which was cleared off the line by Rakish Bingham.
But Accies went further ahead in the 64th minute. Templeton cleverly peeled off at the far post to thrash Imrie’s free-kick low across Bain and into the corner of the net.
Dundee looked down and out but hit back three minutes later. Skondras was penalised for handball as Leitch-Smith tried to go round him, and up stepped the English striker to blast the resultant spot-kick past Woods.
Then, in the 75th minute, Donati was sent off for a second bookable offence as he lashed the ball away in frustration to leave his team-mates under the cosh.
However, the depleted visitors sealed victory with five minutes left when Greg Docherty picked up possession and crossed for substitute Rojano, who only had to tap in from a yard out.