Six minutes later, the hosts were ahead through Garcia. Christian Stuani made a good run down the left before firing across to Garcia, who couldn't miss.
Celta were passing well in midfield but were struggling to create openings, with Espanyol seeing their lead through to the break.
Five minutes after the restart the visitors were almost level when Vadim Demidov was found by Aspas, but he somehow missed the target from close range.
Celta were on the attack and won a series of corners midway through the half, however few real chances were being created.
Lago worked space on the left with 10 minutes to go, but none of his teammates could reach the drilled cross.
Some ferocious challenges were put in by both sides in the closing stages but Espanyol were able to cling on to the win.