In Sunday's other game bottom club Borussia Moenchengladbach thrashed Cologne 5-1, scoring three times in a 10-minute spell before halftime to boost their survival hopes.
Leverkusen, who have been runners-up four times but have never won the Bundesliga, floored St Pauli thanks to a 77th-minute goal from Lars Bender.
Having dominated the first half and seen Arturo Vidal miss an open goal, the home team fell behind just before the hour when Charles Takyi steered in a cross by Florian Bruns to finish a move he had started.
Stefan Kiessling levelled eight minutes later after substitute Eren Derdiyok combined with Gonzalo Castro before pulling the ball back for the German striker to score easily.
Michael Ballack tested Benedikt Pliquett with two powerful drives but the St Pauli goalkeeper could do nothing when Bender beat the offside trap and slotted the ball under him.
Dortmund, held 1-1 at Hamburg SV on Saturday, have 66 points from 29 games while second-placed Leverkusen are on 61. The two teams now look almost certain to take the two available slots in the Champions League next season.
Hanover 96, who recorded a 2-0 win over Mainz 05 on Saturday, are eight points behind Leverkusen in third place, which offers a slot in the Champions League qualifying round.
Champions Bayern Munich dropped to fourth and fired coach Louis van Gaal after their 1-1 draw ath Nuremberg left them fourth, a point behind Hanover.
HEYNCKES MOVE
Leverkusen coach Jupp Heynckes may miss out on the Champions League as he leaves at the end of the season to join Bayern who are poised for Europa League football.
At the other end of the 18-team league, where the bottom two go down, it was an excellent week for Moenchengladbach.
The only team in the bottom four to win, Gladbach moved within two points of 17th-placed St Pauli who trail VfL Wolfsburg, occupying the relegation play-off spot, on goal difference.
VfB Stuttgart, beaten 4-2 by Kaiserslautern on Saturday, are two points ahead of Wolfsburg in 15th.
Venezuela midfielder Juan Arango set Gladbach on their way, netting from Mike Hanke's flick-on in the 29th minute, and Hanke also set up Marco Reus for the second goal five minutes later.
Reus, 21, then scored with a dipping volley before Milivoje Novakovic pulled one back for mid-table Cologne five minutes after the restart.
Filip Daems (penalty) and Havard Nordtveit completed the rout for Gladbach in the second half.
It could have been an ever bigger victory but for a hat-trick of misses from Cameroon forward Mohamadou Idrissou late in the game.
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