There was no Group G final-day reckoning, with places from top to bottom already decided with a game to spare, so Friday's (AEDT) clash was all about playing for pride.
Betis is heading through to the knockout play-offs as runners-up, with Bayer Leverkusen having won the group, while third-placed Celtic have Europa Conference League knockout play-offs ahead of them.
Celtic had gone seven games without a win against Spanish opposition, but goals from Stephen Welsh, Ewan Henderson and David Turnbull, with a winner from the penalty spot in the 78th minute, saw off the LaLiga visitors to Parkhead.
The hosts made a fine start when Welsh deftly headed a left-wing corner from Liel Abada across goal and inside the right post.
Betis midfielder Paul Akouokou struck a sweet shot from outside the box against the angle of post and crossbar with almost the final kick of the first half, and Cristian Tello was denied early in the second half, while Celtic's Nir Bitton scuffed an effort following a corner when he should have done better.
It felt like an equaliser was coming as Joaquin, Diego Lainez and Tello rained more shots towards the Celtic goal. It came in the 69th minute when Joaquin cut in from the right wing, the 40-year-old showing a respectable turn of pace, and Scott Bain pushed a stinging shot from Borja Iglesias against his left-hand post, only for the ball to cruelly ping back into the net off the goalkeeper.
Henderson restored the host's lead three minutes later, touching in fellow substitute Michael Johnston's surface-skimming cross from the right, but the rush of goals continued as Iglesias got in behind the Hoops defence and slotted beyond Bain in the 74th minute.
Celtic had a penalty from their next attack, with Edgar Gonzalez tripping Abada, and Turnbull found the bottom-left corner. Ahead for the third time, this time Celtic locked up at the back, making sure of the win.