Leinster beat Glasgow 18-15 at Celtic Park in May and the defending champion made it seven wins from seven to start the new campaign thanks to a 23-10 success.
It fell 10-3 behind as Ruaridh Jackson took advantage of Hugo Keenan's fourth-minute yellow card with a brace, although neither try was converted.
Cian Kelleher scored a pair of tries himself before the interval and as well as adding the extras on both occasions, Ross Byrne slotted over three penalties.
Glasgow could not even claim a losing bonus point as Leinster kept its host out during 31 phases of play at the end of the game.
Jason Harries's 81st-minute try earned Cardiff Blues a thrilling 31-28 victory over Benetton Treviso.
Treviso led for much of the contest but only one of its four tries was converted whereas the quartet of Cardiff scores each had the extras added.
Connacht kept up the pressure on Conference B leader Munster with a 24-12 victory over Southern Kings, while Conference A's bottom side Zebre claimed its first win of the season, a 39-12 thrashing of the Dragons.
Elsewhere, the Cheetahs claimed a fourth victory of the season, overcoming the Ospreys 18-13.