Saints fell behind in their first Tayside league derby for three years in the 10th minute. Kevin Cuthbert failed to hold an Iain Anderson drive. The ball bounced off the keeper and fell to Simon Lynch, who flicked the ball across the goalmouth where midweek signing Steven Craig dived in to nod home a debut opener.
The Saints hit back almost immediately. With the Dundee fans in full voice, Kevin Rutkiewicz bundled Darren Sheridan's free-kick towards goal but the effort was stifled before the big defender stretched forward and knocked in the rebound to bring his side level.
Just before the half-hour mark, Lynch pulled a shot just wide for Dundee - one of their few scoring opportunities in a game they were determined to defend at all costs.
Saints, on the other hand, pressed forward throughout the match and almost added to their tally in first half injury time, but Goran Stanic amply demonstrated why he is a defender when he blasted his 10-yard shot high over the bar.
Saints had by far the greater possession on both sides of the interval, but just as against Ross County last week they failed to find the move that would prise open their opponents' defence a second time.
An 80th minute shot by Ryan McCann might have put them in the driving seat, but a deflection took it too wide of the mark to leave the sides with a point apiece.