Hammarby made the trip to Trondheim with confidence, having scored an 120th-minute winner away from home to knock out Charleroi in the previous round, winning 2-1 on aggregate.
The visitors began this one by attempting to hit Rosenborg on the counter-attack, and such a move created their best chance of the half, with Sebastian Tounekti cutting in from the left side, but striking the ball too close to Sander Tangvik.
That was the only effort on target in the first 45 minutes, in which the home side had more of the ball, but Jesper Reitan-Sunde and Mikkel Ceide were wasteful with some of their better opportunities.
The second half took longer to ignite - it wasn't until Nahir Besara's strike flew over the bar 20 minutes in that the Lerkendal Stadion saw a shot from either side.
But that proved to be a wake-up call for Rosenborg, who a few minutes later sent a corner deep to Aslak Fonn Witry, who caught the ball sweetly on the volley and forced a good reaction save from Warner Hahn.
However, Hahn was left rooted to the spot on two occasions with time running down - first, space opened up for Iver Fossum to strike from the edge of the area, but the ball flew a whisker wide of the top corner.
Then, with seconds remaining, Hahn watched on as Santeri Vaananen produced an audacious flick which clipped the crossbar and went over.
That was the final chance of the goalless first leg, meaning it will be all to play for when the teams meet again in Stockholm next Thursday.