A couple of minutes later Joao Moutinho smashed his shot on to the PSG side net from inside the area.
Moutinho shot wide moments later for Porto before Ibrahimovic had his attempt from a Jeremy Menez cross tipped over the home side's crossbar by goalkeeper Helton.
Sirigu was called into action in the 28th minute as he pulled off a brilliant save from a Rodriguez shot before Jackson Martínez headed Moutinho's cross over the bar from just yards out.
A minute into the second half, he came close to breaking the deadlock again and then Rodriguez had his powerful shot turned away for a corner.
Porto continued to dominate proceedings and asking questions of the PSG defence, as Rodriguez and Varela put Sirigu under pressure around the hour mark.
The Portuguese giants eventually made all their chances count seven minutes from time when they broke the deadlock.
A superb cross from Moutinho reached Rodriguez at the far post, and he curled it past Sirigu into the PSG net.