Rodolfo Borrell's side secured their first points of this season's tournament with a comfortable win over the Group A leaders at Langtree Park on Tuesday evening
The hosts opened the scoring through Lloyd Jones' header before Adam Morgan doubled their advantage with a well-taken strike from distance. Rosenborg gave themselves a chance of mounting a comeback through Martin Lundal's brilliant half-volley but Morgan struck again to keep things comfortable for the Reds before Jerome Sinclair's last-gasp goal made the result certain.
Liverpool made four changes from the team which suffered a 3-0 defeat to the same opposition in Norway, with Ryan McLaughlin, Jack Roddan, Sam Gainford and Krisztian Adorjan dropping out for Stephen Sama, Conor Coady, Jordan Lussey and Morgan respectively.
Meanwhile, the visitors made three changes, opting to leave two of their goalscorers from the last meeting - Morten Strand and Robin Bjornholm - on the bench.
Both sides were required to show their battling qualities in an opening 15 minutes short of chances. However, the Reds were first to strike a significant blow when Kristoffer Peterson’s slaloming run brought a corner and his subsequent delivery was headed home by Jones.
The goal seemed to settle the hosts, but their attempts to increase their advantage were regularly snuffed out by an obstinate Rosenborg defence. And the Norwegian side almost got themselves apt reward for their defensive solidarity as Sindre Haarberg struck the post with a fine drive from the edge of the box.
But Rodolfo Borrell's side recovered from that blow to work a chance of their own, and they were not to be denied by the woodwork. Jordon Ibe received the ball on the right-hand side before picking out Morgan and the youngster dropped free of his marker with ease to slot the ball into the bottom corner from range.
A second goal cemented the Reds' status as the controlling force in the match and they so nearly grabbed a third when Jakub Sokolik's header was cleared off the line just moments before Marc Pelosi struck the post.
Rosenborg were rocking in the face of early pressure but found a way back into the contest thanks to a moment of individual brilliance. The ball bounced kindly to Lundal on the edge of the box but he still had plenty of work to do in steering the ball over 16-year-old Ryan Fulton into the top corner.
The hosts had to work hard to prevent a swing in momentum, but restored their two-goal advantage when a clever cutback from Pelosi saw Morgan denied, before the latter intelligently brought the ball back from the byline and deceived the defenders to slam home from close range.
Liverpool took their advantage into half-time and came out for the second period looking comfortably in the ascendancy as Coady saw his effort in the box brilliantly saved by Jacob Storevik before failing to keep a header down from the subsequent corner.
Rosenborg largely stemmed the tide from that point on but Storevik had to be alert again to keep a Morgan shot from inside the box out with 20 minutes remaining. But the goalkeeper could provide no further heroics when substitute Sinclair snuck into the box to finish the game off in the final moments.