Lamela got the winner from inside the area by picking up the rebound from Rafa Mir's shot that hit the post after a breakaway three minutes into injury time.
Another Argentinian, De Paul returns to La Liga after joining champions Atletico from Udinese for a reported fee of 35 million euros.
Media reports say the package has cost Tottenham around 21 million pounds ($29 million).
Gil spent last season on loan at Eibar, where he made 29 appearances including 26 top-flight starts.
The Argentine winger was preferred to fit-again playmaker Christian Eriksen by manager Mauricio Pochettino
The gaffer said one start to lose when they start to think negative, and his side is going to enjoy the against Manchester City as it's a fantastic challenge.
Danny Rose and Erik Lamela are back in training with the Tottenham Hotspur first-team squad after long injury lay-offs.