The Paraguay international midfielder recorded a 9.3 player rating in a fine outing at the Amex Stadium, in a season where he appears to have found his scoring touch.
Gomez first tucked in a low cross supplied by Yankuba Minteh, then tallied his second just six minutes later to complete a resounding Brighton victory.
They were the first goals for Gomez in the Premier League this term after scoring four in their EFL Cup third-round rout of Barnsley in September.
Next up for Brighton is a trip to face rivals Crystal Palace at Selhurst Park on Sunday.