The 25-year-old World Player of the Year equalled the record with his first of the night in Seville when he picked up the ball in a central position in the 16th minute and left the Betis defence standing before sending an angled shot across goal into the bottom right corner.
INFOGRAPHICMuller 1972 v Messi 2012
Andres Iniesta's clever back heel set the Argentine up to score again nine minutes later with a sweeping shot from a similar position just inside the penalty area that flew into the same corner of the goal.
"I always say the same, it's nice for what it means but the victory is more important as it maintains our lead over the other teams," a typically modest Messi said in a post-match interview with Spanish TV broadcaster Canal Plus.
"My goal when the year began was to try to achieve everything again, with the team, in the league, the (King's) Cup, the Champions League," he added. "I always start with that idea in mind."
Favourite to secure a fourth successive World Player award when the winner is announced next month, Messi has netted 74 times for Barca and 12 for Argentina in 2012, surpassing Mueller's total for Bayern Munich and Germany in 1972.
He has scored 56 in La Liga, 13 in the Champions League, three in the King's Cup and two in the Spanish Super Cup and still has two league matches and one King's Cup game to add to his tally before the end of the year.
Mueller, known as the "torpedo" while Messi's nickname is "the flea", netted 72 for Bayern and 13 for Germany in 1972 and was 27 when he set the record.
The pair have very different playing styles, with the left-footed Messi scoring many of his goals after trademark weaving runs, while Mueller was more of a poacher inside the box.
Asked about the World Player award, Messi said he would be happy for his Barca team mate Andres Iniesta to win, one of three nominated along with Messi and Real Madrid's Cristiano Ronaldo who won it in 2008.
"Obviously if he (Iniesta) wins it's fully deserved for what he has achieved and what he is as a player, what he does every match," Messi told Canal Plus.
"If he wins it would also be a good thing, it's an award for the entire dressing room."
Messi's double against Betis took his tally in 15 La Liga outings this season to 23 and he became Barca's all-time top league scorer on 192 goals, two more than Cesar Rodriguez.
