The hosts could not have wished for a better start as Ruben Castro put them in front from the penalty spot after just two minutes after Gorka Iraizoz brought down Salva Sevilla.
However, after Adrian produced his first impressive save of the night to turn behind a brilliant volley from Ander Herrera, Athletic levelled four minutes before half-time as Aritz Aduriz showed wonderful composure to scoop Ander's through-ball over the advancing keeper.
Both sides had chances to win it after the break with Jorge Molina the main culprit for the hosts, but it was Adrian who stole the show as he made late saves from Aduriz and Markel Susaeta to ensure his side did not fall to a sixth home defeat of the season.
Athletic started the match just three points above the relegation zone after wins for Granada and Osasuna over the weekend and Marcelo Bielsa's men looked set to be dragged even further into the relegation mix after a terrible opening 10 minutes.
Iraizoz was rightly adjudged to have clipped Sevilla just inside the area in Betis' first attack of the game and Castro gave the keeper no chance with the resulting penalty as he slotted away his 12th league goal of the season.
Castro then had another effort turned away by Iraizoz and Joel Campbell also fired over as Athletic struggled to contain the early Betis onslaught.
But slowly they started to gain a foothold in the game and would have had a spectacular equaliser midway through the half had Adrian not managed to get an outstretched hand to Ander's dipping volley from 25 yards.
The Athletic playmaker did have a hand in the goal when the equaliser arrived, though, as he slipped Aduriz in behind the Betis defence and the former Valencia striker joined Castro as the joint top Spanish goalscorer in the league with a lovely delicate finish from the edge of the area.
Molina then came close on two occasions just after the hour mark as he first volleyed Campbell's cross off-target before heading over a clearer opportunity from another ball in by the Costa Rican.
However, thereafter it was the visitors who dominated and they could count themselves unlucky not to return home with all three points.
Aymeric Laporte was first to threaten with a shot from inside the box that crept just wide before Aduriz was denied by a smart save from Adrian.
Ibai Gomez also fired off-target and Adrian again got down well to turn Susaeta's fierce drive behind as Betis clung on in the final few minutes to restore their three-point gap over Malaga in the race for the final Champions League place.