Real Betis, though, are on the slide having failed to win in five attempts and Pepe Mel watched his charges struggle to convert a handful of half-chances at the El Prat.
The hosts, who were perhaps unlucky not to win by a larger margin, climb to 12th in the table ahead of a daunting trip to Atletico Madrid.
Christian Stuani would be the architect of Espanyol's best moves and he tried his luck within four minutes, his well-struck drive skimming a post.
Three minutes later the Uruguayan surged down the right wing to pick out Garcia, who steered his shot beyond Adrian.
Provider almost turned goalscorer when Stuani met Simao's outswinging corner but his headed effort left much to be desired.
A period of attrition preceded Betis' first real chance in the 27th minute.
This time Francisco Casilla had to look lively as Benat Etxebarria whipped a dangerous corner into the box, the Espanyol keeper punching the ball away from the loitering pack of green shirts.
Stuani drew a firm save from Ruben Perez before Betis missed a gilt-edged chance to level the tie going into the break.
Benat sent Casilla flying across his goalmouth to keep out a devious free-kick after Joan Capdevila had fouled Joel Campbell on the edge of the box.
Betis did not let their new-found momentum slip away at half-time and Francesco Chica tested Perez's responses with a decent chance when play resumed.
Garcia showed Espanyol were still hungry for goals, though, when he worked his way into the area to warm Adrian's palms from close range.
Joan Verdu arrived soon after to give Adrian a more thorough working over but the Betis keeper made himself big once again.
What had often been an end-to-end struggle rapidly descended into a scrappy affair as time ticked away, but there was time for one last moment of drama.
Betis had five minutes left to force an equaliser and Chica was inches away from becoming their hero as his audacious curling volley shaved a post.