Leinster hit back in the second-half through Ireland hooker Sean Cronin, who came on as a replacement. Sexton converted Cronin's try to bring the game within three points.
The European champions attempted to snatch a victory through a quick catch and drive near the Heineken Cup debutants' try-line, but failed.
Soon after, Leinster were awarded a penalty which Sexton coolly slotted a difficult penalty from out wide with the last kick of the game.
Meanwhile Sexton's fly-half rival, Ronan O'Gara landed an 83rd minute drop-goal to steal a 23-21 victory from Northampton at Thomond Park.
Tries from Damien Varley and Doug Howlett helped the two-time Heineken Cup champions to victory. Northampton's Chris Ashton and James Downey scored for the visitors who just missed out on a historic win in Limerick.
Munster went through 41 phases of play in the build up O'Gara's dramatic injury-time winner.
In the same group, the Scarlets' held off an impressive Castres to open their Heineken Cup campaign with a 31-23 win.
Scotland international Sean Lamont was among the try scores as Welsh fly-half Stephen Jones added three penalties and two conversions to Llanelli's total.
Jones' international teammate Rhys Priestland kicked a penalty eight minutes from time was enough to end any hope of a Castres fightback.