Sexton broke Felipe Contepomi’s record of 1,225 points at the Aviva Stadium, landing three penalties and converting both of Rory O’Loughlin’s tries as Leinster joined second-placed Ulster on 23 points in Conference B.
Ian Keatley scored a breakaway try in a first half which ended with Leinster 14-7 to the good and Munster were unable to pull off a fightback despite Keith Earls’ second-half double in front of a crowd of 46,374 in Dublin.
Dan Biggar scored six penalties to pass the 1,500 point mark in the league, but Gareth Davies scored two tries early in the second half and Samson Lee barged his way over for a third as Wayne Pivac’s men claimed the narrowest of victories.
Elsewhere, Benetton Treviso ensured the Southern Kings’ wait for first Pro14 points goes on, easing to a 31-3 victory.
Angelo Esposito claimed a brace of tries, while Marco Barbini and Cherif Traore also crossed the whitewash as the Kings suffered a sixth loss from as many games this season.