With qualification at the top of their Europa League group already secured thanks to Anzhi's draw with Sheriff, the north Londoners scored twice in the second half
Anzhi Makhachkala's draw against Sheriff meant that Spurs were guaranteed to win the group regardless of what happened at the Alfheim Stadion.
And, after dominating large parts of the game without creating a great many chances, an own goal from Adnan Causevic put Tottenham ahead.
Under pressure from Vlad Chiriches, the defender put into his own net from a free kick before Mousa Dembele doubled Spurs' advantage 14 minutes from time, calmly curling home a loose ball in the penalty area.
The Belgian struck the post soon after as he sought to add to his first goal of the season but it remained at 2-0 as Tottenham made it five wins from five matches in the group.
Under-fire manager Andre Villas-Boas made six changes from the last Europa League outing, with three of those coming in the back four - Chiriches, Michael Dawson and Ezekiel Fryers all handed starting berths. Roberto Soldado and Dawson were the only ones to keep their places in the starting XI following Sunday's 6-0 defeat against Manchester City.
Tromso made eight changes from their defeat against Anzhi last time out in the competition. Leading goalscorer Zdenek Ondrasek was back among the line-up, having not featured against the Russian side, while Benny Lekstrom was preferred ahead of Marcus Sahlman in goal.
The hosts threatened within the first minute, as Ondrasek rolled an effort past Brad Friedel's right-hand post after being put through on goal.
Tottenham looked to mount a swift response but an unmarked Etienne Capoue failed to get a touch on Soldado's glancing header in the area.
The visitors grew into the match and Gylfi Sigurdsson was the next to go close, firing wide after collecting a reverse ball from Andros Townsend, before Capoue's sidefooted effort almost deflected past Lekstrom in the Tromso goal.
Soldado threatened to make the breakthrough three minutes after the half-hour mark with a header from Townsend's delivery, before Nacer Chadli fired over when through on goal as Tromso held firm to remain on level terms at the break.
Tottenham continued enjoy much of the possession after the interval but failed to test Lekstrom, with Chadli wasting a good opportunity when he curled high and wide after Townsend had beaten Ruben Kristiansen all ends up on the right.
Eventually, the pressure told for Spurs after 63 minutes due to Causevic's own goal following a Sigurdsson free-kick.
Sigurdsson was also involved in Spurs' second, as his clever pass found Dembele, with the midfielder making no mistake to tuck the ball away neatly and relieve some of the pressure on Villas-Boas, after suffering back-to-back defeats in the Premier League.