Alex Alegria's close-range finish 15 minutes from time looked to be securing all the points for the impressive hosts, but Suarez netted in the final minute to ensure that the champions moved above Sevilla into second spot in the table.
The two goals do not even begin to tell the story, however, with the lack of goal-line technology costing Barcelona the chance to secure all three points as they remain behind Real Madrid in Spain's top flight and having played two games more than the current league leaders.
The big news in the Betis camp was that head coach Victor Sanchez handed debuts to Alin Tosca and Ruben Pardo, who both arrived at the club this month. Central defender Aissa Mandi was also back from Africa Cup of Nations duty and went straight back into the XI, but attackers Antonio Sanabria and Joaquin remained unavailable for selection.
As for Barcelona, with Sergio Busquets, Andres Iniesta and Rafinha on the treatment table, Luis Enrique was forced to select an unfamiliar midfield. Denis Suarez kept his spot following a two-goal showing against Real Sociedad in the Copa del Rey last time out, and the Spaniard was joined by Arda Turan and Ivan Rakitic.
Aleix Vidal and Jeremy Mathieu, meanwhile, were preferred to Javier Mascherano and Sergi Roberto, but there was no rest for Lionel Messi, Luis Suarez and Neymar as Enrique again unleashed MSN despite a busy fixture list.
Barcelona's first half-chance of the match fell to Luis Suarez in the sixth minute when the Uruguay international met a deep cross from Vidal, but Riza Durmisi was on the cover to make a very important block. There was a similar opportunity for Betis down the other end four minutes later, but Gerard Pique just cleared ahead of Ruben Castro.
In the 12th minute, Betis had another half-chance when Digne was forced into a defensive mistake in a dangerous position, but Castro could not find a route past Marc-Andre ter Stegen, who was then forced to make a flying save when the impressive Dani Ceballos looked to pick out the top corner from distance.
Castro again tried his luck for the hosts in the 25th minute after dancing into a dangerous position inside the Barcelona box, but the centre-forward just waited too long to unleash the strike and Pique came out to make the block.
It was Betis that continued to look the more likely to make the breakthrough and Pardo just missed a deep cross from Cristiano Piccini 10 minutes before the break, although Antonio Adan had to make a brilliant save to prevent Neymar from sliding an improving Barcelona ahead in the latter stages of the first period.
Barcelona had a glorious chance to take the lead in the 52nd minute when Messi picked out the right boot of Vidal with a delicious pass, but the full-back's volley just fizzed wide of the far post.
Betis's first opportunity of the second period fell to Alegria in the 55th minute, but the striker could not find a route past Ter Stegen during what was an end-to-end period of the match in Seville.
Andre Gomes for Denis Suarez was Barcelona's first change of the match on the hour, but it was Betis that continued to create openings and Ter Stegen was fortunate to escape without conceding a goal in the 60th minute after having his pocket picked by Castro just outside the box.
Ceballos came within a couple of inches of sending Betis ahead 20 minutes from time when he struck a sensational effort from distance, only to see the ball smash against the crossbar courtesy of a slight touch from Ter Stegen.
Three minutes later, Betis hit the woodwork once again as Castro's low effort crashed against the post, but finally the breakthrough came in the 75th minute when Alegria turned the ball home from close range after a poor punch from Ter Stegen.
Barcelona should have been level 10 minutes from time when Piccini turned towards his own goal, but neither the referee nor the linesman decided that the ball had passed the line when Mandi cleared as the lack of goal-line technology harmed the visitors.
Moments later, the visitors had another glorious chance when Vidal's low cross deflected towards the bottom corner, but Mandi was somehow on hand to clear off the line, before Ter Stegen prevented Castro from making it 2-0 down the other end moments later.
Barcelona would not take no for an answer, however, and sensationally levelled in the final minute of normal time when Luis Suarez collected a cute pass from Messi before sliding the ball into the bottom corner for 1-1.
Next up for Barcelona is a trip to Atletico Madrid for the first leg of their Copa del Rey semi-final on Wednesday night, before returning to La Liga action at home to Athletic Bilbao next weekend. Betis, meanwhile, will look to return to winning ways when they travel to Deportivo La Coruna on February 3.