It was the visitors who took the early initiative when, after 67 seconds, Andy McLaren got to the byline and his cut-back was headed over by Gavin Swankie from close range.
McLaren threatened again after six minutes but his 16-yard shot was well saved by Kenny Arthur in the Thistle goal.
It took Thistle a full ten minutes before they created their first chance. However, the Dundee defence were able to clear.
Thistle did take the lead after 17 minutes after Scott McCulloch played one-twos with firstly Simon Donnelly and then Mark Roberts. And when Roberts received the ball back he turned and shot into the far corner from 18 yards.
Dundee equalised on 27 minutes after McLaren again found his way to the byline. This time his cut-back was met by the onrushing Alex Rae and his shot from 16 yards gave Thistle keeper Arthur no chance.
However, Rae was over-exuberant in his goal celebrations and received his second yellow card, leaving Dundee with only ten men.
As half-time approached, Thistle regained the lead when Craig Sives met a Donnelly corner and headed high into the net on 41 minutes.
The second half saw the visitors battle resolutely, but they could not break down a stubborn Thistle defence – although the hosts had keeper Arthur to thank for a couple of outstanding saves.
Thistle made sure of all three points on 73 minutes when substitute Billy Gibson was fouled in the box by Scott Robertson, allowing Roberts to get his second of the game from the penalty spot.