The Argentina international grabbed the opener in the 16th minute with a trademark dribble and finish to move level with the German striker, who enjoyed his career year in 1972.
His second goal of the evening, and 86th in a remarkable 2012, came with another left-footed shot past Betis goalkeeper Adrian after he had been teed up by Andres Iniesta after 25 minutes.
Betis got back into the contest six minutes before the break as Martin Ruben Castro reduced the arrears from six yards out, converting Alvaro Vadillo's cross from the left.
Betis twice hit the woodwork in the second half but they could not find an equaliser to take the shine of Messi's night.
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Barca remain six points clear of Atletico Madrid, for whom Radamel Falcao scored five times in a 6-0 rout of Deportivo La Coruna.
Diego Costa headed the hosts in front midway through the first half but thereafter it was a one-man show as Falcao stroked home the second moments later before volleying in a wonderful third just before the break.
And the flow of goals for the Colombian continued after half-time as he slotted home a penalty and two more from close range to take his tally for the season to 19.
Real Mallorca's winless streak in all competitions stretched to 12 games as four goals in a 16-minute period either side of half-time saw Levante romp to victory at the Ciutat de Valencia.
The game was well and truly over within 13 minutes of the restart as David Navarro headed home at the back post from a corner before Ruben Garcia and Vicente Iborra also got on the scoresheet after being set-up brilliantly by Martins.
Aritz Aduriz's first-half header earned struggling Athletic Bilbao their first win in four games to lift them away from the relegation zone.
The striker converted Ibai Gomez's cross for his 12th goal in all competitions this season to give the home side some welcome relief, their last three games having yielded just a single point sandwiched between 5-1 defeats to Real Madrid and Barcelona.
The result also took them three points ahead of their opponents, whose attacking threat was limited throughout a lacklustre game.
On Saturday, Real Madrid survived a scare to record a 3-2 win over Real Valladolid, while Malaga cruised to a 4-0 home win over Granada.
New Valencia coach Ernesto Valverde tasted victory in his first La Liga match in charge of Los Che as they beat Osasuna 1-0 courtesy of Roberto Soldado's 56th-minute effort, while Real Sociedad and Getafe played out a 1-1 draw.
Friday's only game saw Alvaro Negredo rescue a point for Sevilla in their 2-2 draw at Espanyol after he came off the bench to score with an injury-time header.
Sunday's La Liga Results
Saturday's La Liga Results
Friday's La Liga Results