The hosts were awarded a penalty inside four minutes when Pape Matar Sarr was clattered by Mats Hummels - a decision which only came to pass after a lengthy VAR check. Son Heung-min stepped up and sent goalkeeper Mile Svilar the wrong way to give Tottenham an early lead.
Midway through the first half though, Roma found a leveller when Paulo Dybala's free-kick from the left channel was met by the head of Evan N'Dicka, who thundered an effort in off the underside of the crossbar. Seconds later, the visitors thought they went in front after Stephan El Shaarawy volleyed one home after a clever dink over the Spurs defence, only for VAR to deny his strike for offside.
An almighty goalmouth scramble saw a combination of Svilar and wing-back Angelino keep out close-range strikes from Brennan Johnson and Dominic Solanke. Shortly after, the Welshman fired his side back in front after sweeping in from a Dejan Kulusevski cut-back.
Kulusevski ought to have added Tottenham's third just after, only to strike the post and then Son to blaze over the rebound from eight yards out.
Twice Roma had the ball in the back of the net at the start of the second half through Artem Dovbyk, but on both occasions he had strayed offside and the celebrations in the away end were cut short. Angelino then crashed a half-volley off the bar, while compatriot Pedro Porro went down the other end and did likewise from a free-kick, while a Solanke header also bounced unfortunately back against the upright.
Porro nearly gifted Roma a late opening with a soft header back towards Fraser Forster, but the goalkeeper was quick off his line to clear the danger. Forster was again called into action in added time to pound away a fierce Gianluca Mancini effort.
But the Tottenham resistance was broken from the following corner when on the second ball, Hummels stabbed home at the far post to snatch a point and send the travelling contingent wild.