Substitute Stefan Kiessling scored the winning goal a minute after entering the action with quarter of an hour remaining, the striker firing home on the rebound after Rosenborg's goalkeeper failed to hold on to Sidney Sam's low cross.
Junior Fernandes and Gonzalo Castro both hit the woodwork for the visitors as Leverkusen emerged as deserved winners in Trondheim.
Leverkusen sporting director Rudi Voller insisted ahead of the match that only a win would do tonight after the German side opened the group with a draw against Metalist Kharkiv.
Rosenborg won their first match against Rapid Vienna to take the upper-hand in the standings, and the visitors were determined not to lose further ground.
Yet it was the hosts who threatened first tonight, just four minutes on the watch when Rade Prica drilled in an effort that drew a good parry from Bernd Leno.
Fernandes served notice of Leverkusen's threat with 25 minutes gone when he unleashed an effort that came back of the crossbar, but within minutes Rosenborg went close again as Prica once more forced Leno into a save.
Ten minutes before the interval Leverkusen threatened through a Lars Bender shot from 20 yards that forced Daniel Orlund into action in the Rosenborg goal.
The second period was a tighter affair than the first but it was the German side that possessed the greater potency in attack, and with 72 minutes gone Sam connected well with a volley that flew over the Rosenborg goal.
The introduction of Kiessling for Fernandes in the 75th minute was to prove the turning point in the contest as within a minute the replacement was tucking the ball home on the rebound after Orlund failed to deal with Sam's ball across the face of goal.
Leverkusen had a golden opportunity to double their lead late on when Bender sprung the offside trap with a cute through-ball for Castro but the winger fired his shot against the foot of the post with only the goalkeeper to beat.