According to Global ESPN, Messi spectacularly sent a free kick under the jumping Alaves wall in the 64th minute to push Barcelona onto 6,000 goals from their 2,801 games since 1929.
Only Real Madrid have scored more goals in the league, with 6,041 in 2,800 games.
After Philippe Coutinho doubled Barcelona's lead in the 83rd minute, Messi scored his second goal of the day with the last kick of the game to increase his all-time La Liga tally to 385 goals -- or 6.4% of all of Barcelona's league goals in their history.
"Sometimes in games like this you have to just wait for Leo to go and do his thing," Barca's Sergi Roberto said. "The first time he hit the bar, the second time, goal number 6,000."
Messi's first goal left teammate Sergio Busquets astounded.
"I had no idea he was going to shoot like that, for us it's spectacular that he has such a range of options," Busquets said.
The Argentine superstar also scored Barcelona's 5,000th goal on Feb. 1, 2009, at Racing Santander.
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