An opportunity to close out a successful first season under Ole Werner knocked for Die Roten Bullen, who made a fast start yet somehow failed to open the scoring in an eighth-minute scramble.
Yan Diomande picked out Christoph Baumgartner inside the area, but both he and Brajan Gruda on the rebound were denied from point-blank range by Nikola Vasilj, before the offside Ridle Baku missed an open goal from little more than a yard out.
The visitors settled from there, and they came close to breaking the deadlock themselves when Eric Smith’s free-kick whistled just wide of the target.
Alexander Blessin’s men offered considerable threat on the break, and that ought to have yielded the opener when Andréas Hountondji laid on for Martijn Kaars, but he could only rifle his first-time effort off the crossbar.
The St Pauli forward paid a heavy price for that miss, as in the final minute of the half, Leipzig hit the front.
David Raum’s corner dropped favourably for Xaver Schlager on the six-yard line, and the midfielder duly turned home via the underside of the bar in his final home games for the club.
That proved the ultimate sucker-punch for Die Kiezkicker, who were fortunate not to fall two behind within 10 minutes of the restart.
Baumgartner released Diomande, who in turn teed up Assan Ouédraogo, but the young midfielder could only direct his strike against the base of the post.
Just moments later, another Raum corner caught the visitors out when the unmarked Willi Orbán got ahead of the front post and steered a brilliant header across goal and into the far corner.
St Pauli threatened to unravel from there, with Gruda seeing a goal chalked off for offside before Baumgartner smashed over from a promising position.
Leipzig had looked exceedingly comfortable, but Abdoulie Ceesay cast the result into doubt when he surged clear of the home defence and slotted home a goal that halved the visitors’ arrears.
That denied Die Roten Bullen just a second clean sheet in 14 league matches, but they held on for a fifth successive home victory regardless.
It’s a damaging defeat for St Pauli, though, with their winless run reaching nine matches ahead of next week’s potentially decisive clash with 16th-placed VfL Wolfsburg, who they trail on goal difference, having played a game more.
Flashscore Man of the Match: Willi Orbán (RB Leipzig)