But the win came at a cost as Mousa Dembele, Danny Rose and Younes Kaboul all came off injured.
Andre Villas-Boas had accused the Football League of putting his players' careers in danger with their scheduling of the Capital One Cup, but it was the low-key European clash against Tromso that claimed three injury victims.
Rose pulled up with what looked like a hamstring injury in the first half and Dembele had to be carried off on a stretcher after being kicked from behind by Lars Gunnar Johnsen.
Tottenham finished the game with 10 men as Kaboul hobbled off five minutes from time when Villas-Boas had made all of his substitutions.
Tottenham's summer spending spree means Villas-Boas is well-equipped to withstand the injury losses but, with two games coming up in the next five days, the timing is hardly ideal.
With no senior specialist left-back available, replacing Rose will be the Portuguese's biggest task.
The injuries took the gloss off a good night for Spurs although Tromso, who only made the group stages because of Besiktas' disqualification for match-fixing, were very poor.
Defoe is now one goal short of moving up to fifth in the all-time top scorers' list following his two well-taken strikes and Christian Eriksen's first goal for Spurs was a joy to behold.
Debutant Erik Lamela showed why Spurs shelled out £26million for his services early on, opening his box of tricks to flick the ball past Thomas Drage, but his final ball went to waste.
The game went quiet for 10 minutes as Tromso kept Tottenham at bay, but a couple of incisive passes from Lewis Holtby and Lamela carved open the Norwegians' back four and Defoe calmly lifted the ball over Marcus Sahlman.
Six minutes later and Defoe had his second. Holtby was involved again, picking the ball up off Gylfi Sigurdsson before picking out Defoe and he rolled the ball between the legs of Jaroslaw Fojut and the Tromso goalkeeper.
Tromso looked every inch the whipping boys of Group K as they failed to get out of their own half.
Everything was going perfectly for Spurs until the 35th minute when Rose unexpectedly pulled up with an injury to his right leg and hobbled off.
Substitute Jan Vertonghen slotted in perfectly at left-back and Spurs continued to control the game.
Defoe and Holtby exchanged passes before finding Sigurdsson in the box, but the Icelandic midfielder dragged his shot wide.
Drage shot high and wide in Tromso's first effort on goal while Holtby smacked a 25-yard shot just wide in injury time.
Villas-Boas' injury problems continued to mount after the restart when substitute Johnsen kicked out at Dembele's standing leg while the Belgian was shielding the ball.
Dembele collapsed on the floor, writhing in pain and he had to be carried off on a stretcher clutching his right leg.
Johnsen entered the book and Eriksen came on for the Belgian.
Sandro almost scored a rare goal with 20 minutes to go, but Sahlman was equal to the Brazilian's header.
Villas-Boas brought on Paulinho for Lewis Holtby, who received a warm round of applause.
More injury problems followed for Villas-Boas as Kaboul waved to the bench after suffering an injury, but he had to stay on for a while as Tottenham had used all three substitutions.
Lamela's slip allowed Morten Moldskred to break down the right on a rare Tromso attack, but the Argentinian recovered to deny the winger.
The game looked in danger of petering out until Kyle Naughton found Eriksen on the edge of the box and he clipped a wonderful dipping shot over Sahlman.
With the result now beyond doubt, there was no need for Kaboul to continue and he hobbled off.
|Tottenham Hotspur||Team Statistics||Tromsø|
|2||1st Half Goals||0|
|8||Shots on Target||0|
|7||Shots off Target||2|
|70.1||1st Half Poss.||29.9|
|74.7||2nd Half Poss.||25.3|