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City had the game's first opportunity with just four minutes on the clock, Jesus Navas finding Aguero after some fine work, with the Argentine clipping the outside of the post with his angled drive.
The hosts nearly doubled their advantage on the 20-minute mark, though Lloris got a big hand to Aguero's header from six yards out following a Gael Clichy cross to save his side.
Continuing their pressure, City again came close to adding a second, this time through Martin Demichelis. He glanced Silva's cross towards goal, only for Danny Rose to clear away off the line.
Spurs did have the ball in the back of the net before the interval, though it was ruled out after Michael Dawson was adjudged to have been offside.
The half ended on a sour note for Manuel Pellegrini's side with Aguero departing the pitch through injury.