Argentine forward Gomez found the space to blast in after an impressive solo run with 20 minutes to go with new arrival Anthony Martial teeing up Rafa Mir to head in a second five minutes later.
Second-placed Sevilla ended a series of three consecutive draws to move three points behind Real Madrid who play at Villarreal, sitting sixth, on Saturday.
Sevilla's run of draws had allowed Real to preserve a healthy lead at the top of the table, despite Carlo Ancelotti's side only winning two of their last four games.
Injuries had played a part in Sevilla's dip while Ivan Rakitic missing an injury-time penalty in the goalless draw with Osasuna last weekend was particularly hard to take.
Martial, who joined on loan from Manchester United in January, was supposed to provide some freshness.