Former Swansea striker Bafetimbi Gomis thought he had earned the visitors an unlikely late win but his sublime finish was ruled out for offside.
Memphis Depay twice went close to giving Xavi’s side a first-half lead.
The Dutchman’s curling free-kick was saved by Galatasaray goalkeeper Inaki Pena, before Depay was denied again by the Barcelona loanee with a low drive that was heading for the far corner.
Jordi Alba also sent a first-time effort inches wide of the far post as Galatasaray held on to keep the tie level ahead of next week’s second leg in Turkey.
