Prop Stephen Knoop returns to a strong-looking replacements bench alongside the likes of Jennings and Jonathan Sexton, who impressed at out-half after coming on for O'Driscoll last Friday.
Leinster have ground to make up in Pool 6 after being turned over in Toulouse last month but they will be boosted by their '16th man' tomorrow night with a capacity crowd of 18,500 set to turn up at the RDS.
Commenting on his side's form and that of opponents Edinburgh, Cheika said: "Part of the test this week is making sure we're switched on to improving our performance. It was good to have a couple of wins (against the Ospreys and Munster) but if you stay still, people will overtake you.
"Everyone's acutely aware that we have to put that Munster game behind us pretty quickly. We've just got to concentrate on the challenge ahead of us.
"I think Edinburgh are going to come and try to smash us. They'll come here with no inhibitions.
"If you knock off him for a second he'll be through your line so we've got to be aware of him.
"We have watched three or four games together to try and get a strategy. They've gotten some good results, almost beating Munster down at Musgrave Park and beating the Scarlets at home and Ulster away, so they've got some form running in together. When you watch them they play good footy.
"They can play wide and can play it tight. They've got a mauling game, with a good breakout. They've also got a killer of a guy on the floor in (Ross) Rennie who can slow you down. He has put us to the sword a few times before."
LEINSTER (v Edinburgh): Rob Kearney; Shane Horgan, Brian O'Driscoll (capt), Gordon D'Arcy, Luke Fitzgerald; Felipe Contepomi, Cillian Willis; Ollie Le Roux, Bernard Jackman, Stan Wright, Leo Cullen, Malcolm O'Kelly, Stephen Keogh, Keith Gleeson, Jamie Heaslip.
Replacements: Brian Blaney, Stephen Knoop, Cameron Jowitt, Shane Jennings, Chris Keane, Jonathan Sexton, Gary Brown.