It should have been even better for Messi, who missed a penalty early on, stunning a fiercely pro-Argentina 70,649 crowd at the air-conditioned home of the Dallas Cowboys.
“Very happy for the victory, it was very important, hard, hard, hard, and it gives us peace of mind for what is to come,” Messi, who is in his sixth World Cup appearance, told broadcasters.
“The match was even, intense and we are happy to get six points.”
Messi’s name rang out along the concourses of the stadium after another virtuoso display.
“There is not much to say about Leo. More than 20 years of being the best in the world, he is the best in history,” striker Julian Alvarez said.
With both sides knowing a win would put them into the knockout rounds with a game to spare, Lautaro Martinez was brought down in the box, sandwiched by two Austrian players.
Referee Amin Mohamed gave a penalty after a VAR intervention, and a wall of noise went up as Messi stepped forward on nine minutes.
But his run-up was slow and his weak effort off target, dragging it wide.
For all his brilliance, Messi — who turns 39 on Wednesday — is surprisingly poor from the penalty spot by his standards.
He also saw his spot-kick saved by Wojciech Szczesny in a 2-0 win over Poland at the 2022 World Cup, where Argentina went on to be champions, and missed at the 2018 tournament.
In the 19th minute Messi had a clear sniff at goal, only for Austria captain David Alaba to steal the ball off his toes at the last moment as he danced through.