Messi took just 16 minutes to equal German legend Gerd Muller's mark of 85 from 1972 when he slotted a ball from Adriano into the corner.
And the 25-year-old surpassed Muller nine minutes later with a sweeping shot he was afforded by Andres Iniesta's deft backheel.
But the player himself was more focused on the fact that the win maintains Barca's six-point lead over Atletico Madrid at the top of La Liga.
"I've said it a lot, it's nice to beat records but the win for the team is what is important and the points difference at the top," said Messi.
"My goals are to win titles with the team, the Spanish league, Spanish Cup or Champions League is more important than any personal records."
Sunday's milestone was the latest in a jaw-dropping, relentless career.
Last season, he became the most successful goalscorer in the history of the La Liga by hitting 50 goals in the league campaign and also equalled the record for goals scored in a Champions League season when he netted 14 times.
He is already the club's greatest scorer having eclipsed the record held by Cesar Rodriguez set in the 1940s and 1950s.
This latest feat means he will be the overwhelming favourite to once again claim the FIFA Ballon d'Or over team-mate Iniesta and Real Madrid's Cristiano Ronaldo.
He would be the first player to win the award four times.