Holders Leinster had the bonus point in the bag by half-time as they overran Glasgow in Sunday's Pool Three clash.
Centre Eoin O'Malley, the only man in the Leinster team without an international cap, scored two tries.
Full-back Rob Kearney got things going with a fourth-minute touchdown and Gordon D'Arcy got in to secure the extra point just before half-time.
Glasgow's Henry Pyrgos breached the home defence in the 74th minute but Leinster's Isaac Boss got the last try.
It was a strong performance by Leinster who made light of Brian O'Driscoll's absence against a team which had beaten Bath a week earlier.
The Irish province, who drew away to Montpellier on the opening weekend, take over from the Scottish club at the top of the pool with seven points from two games.
They now face back-to-back games against Bath in December.
The outcome was in little doubt from the moment Kearney finished off in the corner after Jonathan Sexton's cross-field kick had been caught by Isa Nacewa.
Sexton landed the conversion from the right touchline and made it 10-0 with a 16th-minute penalty.
A line-out infringement saw Devin Toner banished to the bin but Leinster managed 17 points without reply while their towering lock was kicking his heels.
O'Malley, O'Driscoll's deputy at outside centre, scored under the posts after Leinster opted not to convert an easy penalty and instead piled pressure on the Glasgow line.
The home pack surged forward again, the back setting up the chance for D'Arcy to offload for O'Malley to snaffle his second try.
Just before the break, Leinster's driving maul had Glasgow on the retreat once more and D'Arcy got over from Nacewa's pass.
The second half was scoreless until the 74th minute minute when replacement Pyrgos breezed through for a try which Weir converted.
That was a jolt for Leinster and they summoned a response with former Ulster scrum-half Boss getting over for his team's fifth try.
Leinster: R Kearney, Nacewa, O'Malley, D'Arcy, Fitzgerald, J Sexton, Reddan, van der Merwe, Cronin, Ross, Cullen, Toner, McLaughlin, O'Brien, Heaslip.
Replacements: Carr for D'Arcy (57), Madigan for J Sexton (61), Boss for Reddan (61), Healy for van der Merwe (48), Strauss for Cronin (61), White for Ross (57), R Ruddock for McLaughlin (66), Jennings for O'Brien (54).
Glasgow: Hogg, Seymour, Murchie, Morrison, Shaw, Weir, Cusiter, Grant, MacArthur, Cusack, Gray, Kellock, Harley, Barclay, Wilson.
Replacements: Nathan for Murchie (66), Aramburu for Shaw (59), Welsh for Grant (66), Gillies for MacArthur (66), Pyrgos for Cusack (61), Ryder for Kellock (54), Fusaro for Barclay (41).
Not used: Kalman.
Referee: Andrew Small (England)
Att: 17,924
