Navarro joined Paolo di Canio's team from the Seagulls just two months ago and hit a second-half brace after Paul Benson had given the Robins the lead.
The home side started brightly and had a chance in the first minute when Jay McEveley crossed for Andy Williams who put his header from eight yards high and wide.
Brighton had a goal disallowed after on-loan full-back Wayne Bridge crossed for Ashley Barnes who headed in but the effort was ruled out for a push on McEveley.
Striker Barnes came close soon after when he headed Vicente's corner against the left-hand post and out for a goal kick.
Benson struck eight minutes after the interval, converting Navarro's neat training ground free-kick from six yards out.
Navarro doubled their lead 12 minutes later when he slammed home from eight yards after being set up by birthday boy Williams.
Midfielder Navarro netted again just 10 minutes later, hitting a deflected 20-yard strike past former Manchester United goalkeeper Tomasz Kuszczak.
Di Canio had plenty to celebrate at the end but for opposite number Gus Poyet there look to be problems to solve before the start of the npower Championship season this weekend.