With the injured Cristiano Ronaldo watching-on from the stands, Madrid appeared to settle for a draw from early-on – although City keeper Joe Hart was still called-on to make a crucial save in the closing stages when he blocked a close-range shot from Pepe.
Last night's result means that a 1-1 finish in the second leg next week would send Manuel Pellegrini's team through to the final.
He says they won't fear facing the Spanish giants in their own yard.
The second-leg takes place in Madrid next Wednesday.
Later tonight, the second semi-final gets underway.
After knocking-out defending champions Barcelona in the quarter-finals, Atletico Madrid will play host to Bayern Munich tonight, with kick-off at 19:45.
