Finishing top of the group was already secured due to the outcome of Anji's encounter with Sheriff earlier in the night - it finished 1-1 in Russia - but an own goal from Adnan Causevic and a Mousa Dembele strike saw to it that a further three points were banked.
It was Dembele's first goal since his crucial strike against Lyon in this competition in February.
Tromso managed to weave a route through our defence after just 40 seconds when Zdenek Ondrasek found himself through on goal, but he panicked a little and shot wide.
The conditions were more than tricky, the snow fell just before kick-off and the roll of the ball on the artificial surface was proving hard to judge.
On 14 minutes there was half a chance when a Gylfi Sigurdsson corner was flicked on at the near post by Roberto Soldado and Etienne Capoue was not too far away sliding in at the far post. Four minutes later Sigurdsson fired narrowly wide after being teed up by Andros Townsend following good work by Vlad Chiriches.
Capoue nearly opened the scoring with a deflected shot after a clever passage of play with the players adapting to the conditions. Townsend then worked keeper Benny Lekstrom low to his left.
Sigurdsson and Townsend combined to provide Capoue with a headed chance that flew just wide despite the best attempts of Sigurdsson to bring it back into the play. Nacer Chadli should have opened the scoring when through on 38 minutes but shot over.
The second half began in a lively fashion after the pitch was 'hoovered' during the break, but there was a lack of precision in key areas from both sides and this was not a night where goalkeepers were forced to dive around.
What we did know at half-time was that the group was won following a draw between Anji and Sheriff.
The ball was in the net on 54 minutes via Sigurdsson, but it was not to be as Soldado was adjudged to have used an arm to control a Townsend cross before laying back across goal.
The deadlock was broken on 62 minutes when a low free-kick from the left by Sigurdsson was met by Chiriches and helped in by Causevic as he tried to thwart the Romanian.
Eight minutes later Jan Vertonghen came on in place of Zeki Fryers at left-back, with Lewis Holtby taking over from Chadli.
On 75 minutes, Sigurdsson squeezed the ball into the path of Dembele, who shot past Lekstrom to double the advantage. He was through again moments later seizing on a Soldado through ball, but this time struck the inside of the post, before failing to convert the rebound from a tight angle.
Erik Lamela then came on for the excellent Sigurdsson and the team were pinging the ball around with authority when the final whistle blew.
Tromso (4-4-2): Lekstrom; Frantzen (Norbye, 68), Fojut, Causevic, Kristiansen; Andersen, Johansen, Bendiksen (Helmke, 77), Drage; Ondrasek, Moldskred (Espejord, 71). Subs not used: Bakkelund, L Johnsen, M Johnsen, Antonsen.
Spurs (4-2-3-1): Friedel; Naughton, Chiriches, Dawson, Fryers (Vertonghen, 72); Capoue, Dembele; Chadli (Holtby, 72), Townsend, Sigurdsson (Lamela, 78); Soldado. Subs not used: Archer, Fredericks, McEvoy, Coulthirst.
Yellow cards: Tromso - Fojut. Spurs - Capoue, Dawson, Soldado.
Goals: Spurs - Causevic OG (63), Dembele (76).
Referee: Mr I Aranovskyi (Ukraine).