Without their Ireland contingent and Argentinian talisman Felipe Contepomi, Leinster still had enough firepower to see off Warriors.
Samoan prop Fosi Pala’amo and former Wallaby scrum-half Chris Whitaker scored their first tries for Leinster.
Glasgow took an 18-16 lead into the break with tries from Jon Petrie and Thom Evans, but could only add a Kevin Tkachuk effort as Leinster dominated the second half.
Rob Kearney, kicking in the absence of Contepomi, landed a fourth-minute penalty to get Leinster off the mark.
On 12 minutes, 6ft 10in Devin Toner sucked in a lineout ball and Pala’amo was mauled over.
Kearney missed the conversion. Dan Parks replied with a penalty, but Leinster gained further control in the 28th minute. Hefin O’Hare fumbled a kick ahead from replacement Andrew Dunne and hooker Brian Blaney dribbled forward to touch down.
Dunne put his conversion attempt wide and Glasgow gained a foothold to take a lead into the break.
On 33 minutes, a clever switch by Parks out to the right allowed Petrie to squeeze in at the corner.
Parks converted and, two minutes before the interval, a botched Leinster lineout saw Evans score in the left corner.
Cheika was fuming moments later when a legitimate try from Denis Hickie was ruled out for crossing.
Kearney’s injury-time penalty cut the gap to two points.
A bulldozing run from Pala’amo, two minutes after the restart, let Hickie in and put Leinster back in front.
Three minutes later, prop Tkachuk powered over from close range.
Kearney then kicked a penalty, and a flurry of recycles saw Whitaker scamper through on the hour mark.
On 80 minutes Jamie Heaslip crowned his night as stand-in captain with a fifth try.
Fitzgerald, Kearney, Lewis, Berne (Dunne 57), Hickie, Warner, Whitaker, McCormack (Corrigan 40), Blaney (Vermaas 75), Pala’amo, Hogan (Byrnes 80), Toner, Keogh (Ronan 77), Gleeson, Heaslip.
Lamont, O’Hare, Morrison, Henderson, Evans, Parks, Beveridge (Pinder 69), Tkachuk, Thomson (Mulligan 53), Low (Prescott 58), Newman, Kellock (Turner 9), Wilson, Barclay, Petrie (Swindall 62).
J Jones (RFU)
Borders 13 Llanelli Scarlets 19; Newport Gwent Dragons 17 Edinburgh 10
Bristol 15 Sale 9; London Irish 11 Gloucester 22; Newcastle 3 Harlequins 14.