Betis enjoyed the better start in a cagey opening to the match, but the visitors wasted the first clear chance midway through the first half when Alfred N'Diaye could only miscue an effort straight at Sergio Alvarez from close range.
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The hosts continued to see more of the ball than Celta, but they struggled to create opportunities in the final third heading into the break.
Betis were offered a route back into the game early in the second half as Jonny foolishly gave the ball away in a dangerous position before pulling back Petros to give the referee no other option than to show him a straight red card.
Joaquin threatened to capitalise just moments later, but his free kick came back off the post to the frustration of the home supporters.
Inevitably, Betis put the Celta defence under long spells of pressure but the 10 men battled impressively to limit the chances on offer.
Ruben Castro should have scored the equaliser after finding space between defenders in the box, but he could only head wide from Cristiano Piccini's inviting delivery.
Despite the admirable efforts of Celta, they were unable to keep out the hosts as Petros produced an inch-perfect through ball to find Jorge Molinas, who poked home to secure a point for Betis.