It looked like the English side would walk away with a point after Hugo Lloris made a superb late save to thwart Pedro Porro.
But Paulinho came from the resulting corner in the 90th minute and Brazilian Arthur Gomes came off the bench to make it 2-0 with an excellent solo in injury time.
“It was a tough result. If you lose the game, you’re not happy,” admitted Conte.
Sporting led the group with six points, while Eintracht Frankfurt gave Spurs three points thanks to a 1-0 win at Marseille, with Jesper Lindstrom scoring in the first half.
Leverkusen picked up their first Group B points by beating Atletico Madrid 2-0 with two late goals, Robert Andrich and Moussa Diaby both scoring.
Belgian champions Club Brugge top the group with six points after an impressive 4-0 victory at FC Porto.
Former Barcelona striker Ferran Jutgla opened the scoring with a penalty before Kamal Sowah, Andreas Skov Olsen and Norwegian teenager Antonio Nusa all netted in the second half.