As a team, UCLA is in seventh place (+10, 578), shooting a 4-over 288, two strokes better than Friday.
The Bruins are just 12 shots back of first place.
All six Bruin newcomers will play at this weekend's Stanford Intercollegiate.
Tavatanakit has won three times on the Symetra Tour this season.
The Bruins improved 16 shots from their first round to their final round.