Aleix Alegria gave Betis the lead their dominance deserved 15 minutes from time when he bundled home from close range after Marc-Andre ter Stegen flapped at a corner.
However, Barca were rightly infuriated seconds later as the ball clearly crossed the Betis goalline, but no goal was given by referee Alejandro Jose Hernandez.
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Suarez did at least rescue a point in the dying seconds, though, as he slotted home Lionel Messi's through ball for his 21st goal of the season.
Barca move above Sevilla into second on goal difference, but remain a point adrift of Real Madrid, who have two games in hand, the first of which comes at home to Real Sociedad later on Sunday, whereas Sevilla are also in action later at Espanyol.
Barca boss Luis Enrique paid the price for again heavily rotating his side with Wednesday's Copa del Rey semi-final, first leg at Atletico Madrid in mind.
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Enrique made six changes in all, including three of the back four and Betis took advantage with a bright start.
Ter Stegen was forced into saves from Ruben Castro and Dani Ceballos early on.
However, Barca arguably had the best chance of the first-half when Antonio Adan flew off his line to deny Neymar from another scintillating Messi pass.
Enrique made all three of his substitutions early in the second period, but Barca were still struggling to gain a foothold under Betis' intense pressing.
Ceballos saw a dipping long-range effort come back off the bar before Castro struck the post with Ter Stegen beaten at his near post.
The German goalkeeper had a moment to forget for the opening goal as he failed to get a good connection on an attempted punch under pressure from two Betis players and the ball fell kindly for Alegria to tap home.
Conceding appeared to wake Barca from their slumber and they were doubly denied by Hernandez seconds later as Neymar went down inside the area and the ball ricocheted towards the Betis goal.
Replays showed the ball clearly went over the line before Alissa Mandi cleared, but La Liga's refusal to implement goal line technology due to pricing fears cost Barca dearly as no goal was given.
Another goal line clearance prevented Aleix Vidal's deflected cross levelling for Barca moments later.
Betis should have sealed the three points when Castro broke clear on goal eight minutes from time, but Ter Stegen redeemed himself with a fine save.
And that miss proved crucial as Messi finally found the space to slip a pass through the Betis defence and Suarez dispatched the ball into the far corner.
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