The match was not short of drama and one early talking point would be the knee injury sustained to Andres Iniesta who had to be stretchered off.
Lionel Messi then opened the scoring midway through the first half with a well struck effort and Barcelona went into the break 1-0 up.
However, Valencia then staged a second half fightback when on-loan Barcelona striker Munir scored against his parent club and then Rodrigo finished well to put the home side ahead just before the hour mark.
Barcelona were't behind for long, though, and Suarez equalized after Diego Alves parried Ivan Rakitic's header into the Uruguayan's path.
When the match appeared to be heading for a draw, Barcelona got a penalty in the second minute of two added minutes when Suarez was brought down in the box. Messi converted the penalty, despite Alves getting close and Barcelona took the three points back to Catalonia.