The Golden Bears (20-13) will play top-seeded Baylor, which set an NCAA Women's Tournament record for margin of victory when it beat Texas Southern 119-30 on Saturday.
The Tigers finished 20-12.
Kristine Anigwe scored 13 of her 15 points in the second half for Cal.
Alexis Hyder, Rina Hill, Chloe Jackson and Raigyne Moncrief led LSU with 10 points each.
The score was tied twice early in the fourth quarter before LSU took its first lead of the game, 45-43, with 7:19 left.
Anigwe's three-point play and two more free throws gave Cal a 48-45 lead.
After Ayana Mitchell made a free throw for the Tigers, CJ West made a layup for the Bears.
Mitchell and Moncrief each made a free throw and Mitchell made a basket to tie the score at 50 with 2:54 left.
Thomas broke the tie with a 3-pointer, but Jackson made a jumper to get LSU within a point with one minute left.
Hyder missed a jumper with 14 seconds left. Anidwe made two free throws with seven seconds left and Moncrief missed a 3-pointer with two seconds left.
Six different Bears scored as they took an early 13-4 lead as 10 of their points came from the paint.
Shanice Norton made two free throws for LSU, but Mikayla Cowling made a 3-pointer as Cal rebuilt its lead to nine at 18-9 after the first quarter.
The Tigers got within 24-18 on Hyder's basket and she made another basket that cut the Bears' lead to 31-25 at halftime.
Cal made 13 of 26 shots in the first half and LSU made 9 of 32, but the Bears committed 10 turnovers and the Tigers five.
Hill started the second half scoring with a jumper that got LSU within four. Cal pushed the lead to nine before Moncrief, the Tigers' leading scorer, made a basket after missing her first nine.
Moncrief made two more baskets and LSU got within 38-35.
Jackson's jumper got the Tigers even at 39 before Thomas made two free throws, giving Cal a 41-39 lead after three quarters.