The Gunners will take a commanding lead into the second leg of their Europa League semi-final in Spain next week but they had to fight back from a goal down after Mouctar Diakhaby's header put Valencia ahead after just 11 minutes.
Arsenal weren't behind for long however, as Lacazette slotted in Pierre-Emerick Aubameyang's pass and the Frenchman grabbed his second on 21 minutes when he headed home Granit Xhaka's cross.
Lacazette could, and probably should, have completed a hat-trick but he miscued a header from close range and was later denied twice by visiting keeper Neto.
Arsenal were not to be denied a third though as an Aubameyang volley in injury time secured a two-goal lead ahead of next week's trip to the Mestalla.
Los Che will still feel they are in this tie thanks to their away goal, but Arsenal are in an excellent position to secure a place in the final after their 3-1 win in North London on Thursday night.