- Paulinho (90')
- Arthur Gomes (90'+3')
Spurs were unable to find their rhythm in the game and struggled to create many opportunities before eventually being punished by the hosts.
It is the first time in Sporting's history where they have won their opening two Champions League games.
The victory means Sporting lead Group D with six points, with Spurs second on three after two games.
Spurs coach Antonio Conte was unhappy with the way his side collapsed at the end of a tricky encounter.
"For sure we are frustrated because the game was balanced and we tried to win the game in the second half," he said.
"But in the last 10 minutes we can do much better. They score with a corner, then we conceded the second goal after the 90 minutes. It's a pity, a difficult game for sure."
There was a minute's silence to commemorate the death of Queen Elizabeth II, which led to all matches in the United Kingdom scheduled for last weekend being postponed and leaving Spurs with extra time to prepare for the trip to Portugal.
Moments later, former Spurs trainee Marcus Edwards almost scored a remarkable individual goal, dancing his way from the halfway line into the area before playing a one-two with Francisco Trincao and then shooting at goal, only to be denied by the leg of goalkeeper Hugo Lloris.
The game looked to be heading for a draw until Sporting midfielder Pedro Porro went on a late marauding run and curled a shot towards goal which Lloris just managed to tip over the bar.
Sporting striker Paulinho then broke the deadlock in the 90th minute with a glancing header from a corner.
Brazilian forward Gomes, who had only come onto the pitch after the goal, made sure of the victory with a superb strike in the second minute of added time, finishing from close range after a breathtaking run into the box.
Spurs host struggling Leicester City in their next Premier league game, returning to European action at Eintracht Frankfurt on Oct. 4, when Sporting play away to Marseille.
"It feels great. Winning like that at the end, after we put in a hard shift, we couldn't be happier," said Sporting forward Edwards, who started out as a trainee at Spurs. "We deserved it. We showed how we can play."
Information from Reuters was included in this report.
- Srdjan Jovanovic