Brazil also have the maximum six points from two games after a superb 90th-minute winner from Marquinhos against Peru in Lima for the only goal of the match.
But Marcelo Bielsa's Uruguay suffered a setback, giving up the lead to end with a 2-1 defeat at Ecuador.
Messi, who has had a hectic schedule with his club Inter Miami, watched his teammates from the bench but was not listed as a substitute, having complained of tiredness after scoring the winner in Thursday's 1-0 victory over Ecuador.
Despite the absence of their talisman Lionel Scaloni's side had too much firepower for Bolivia with goals from Enzo Fernandez, Nicolas Tagliafico and Nicolas Gonzalez securing an impressive victory.
Chelsea midfielder Fernandez went close with a wonderful effort from 30 yards out superbly saved by Guillermo Viscarra, who then did well again to keep out a near-post drive from Julian Alvarez.
The lively Alvarez had a hand in Argentina's opener in the 31st minute, feeding Angel Di Maria, whose low cross was turned in by Fernandez, who had made a perfectly timed run into the box.
Eight minutes later Bolivia's task got even tougher when Roberto Fernandez was sent off for an over-the-top challenge on Cristian Romero.
Argentina went in at the break with a 2-0 lead after Tagliafico met a floated Di Maria free-kick with a header that looped over Viscarra.
The three-time World Cup winners were in total control after the break with Alvarez hitting the post in the 70th minute and Viscarra kept busy by efforts from Rodrigo De Paul and Di Maria.
Gonzalez wrapped up the victory seven minutes from the end with a left-footed drive after more hesitant defending from the home side, who have lost both their opening games.
Scaloni was pleased with the performance by his team, saying they were "not afraid to play with the ball" and also offered an explanation for Messi's absence.
"Leo was not ready to play, he tried to recover, but he did not feel comfortable," he said.
- Masterful Marquinhos -
Brazil came up against a determined Peru side and looked set to be frustrated when Raphinha's rocket in the 72nd minute was brilliantly saved by Pedro Gallese.
But in the final minute Neymar whipped in a corner and Marquinhos met it with a masterful glancing header that flashed into the far corner.
Colombia had to settle for a point in a disappointing goalless draw in Santiago, Chile.
Chile, with Alexis Sanchez back in the starting line-up, had the better of the game, playing some intelligent football in possession but like their opponents they lacked a cutting edge.
After an impressive start to his reign in charge of Uruguay, Argentine Bielsa saw his team lose to two goals from Ecuador defender Felix Torres in Quito.
Uruguay took the lead in the 38th minute through Agustin Canobbio but the home side levelled just before the break when Torres rose to power home a header from a Moises Caicedo cross.
A penalty award gave Ecuador the opportunity to take the lead after the break but Enner Valencia's woeful effort from the spot flew wide.
But Torres showed his value again to grab the winner, sliding into a crowded box to turn in a low cross from 16-year-old Kendry Paez.
- VAR drama -
Venezuela defeated Paraguay 1-0 at home thanks to Salomon Rondon's injury-time penalty to raise hopes of making the World Cup for the first time in their history.
The hosts thought they had the lead in the 78th minute when Yangel Herrera fired home, but the referee's review at the monitor concluded that the midfielder had handled the ball -- to the fury of the home crowd.
But the technology worked in Venezuela's favor in stoppage time when it spotted that Paraguay defender Ivan Piris had handled during an aerial challenge in the box and Rondon confidently tucked away the spot-kick.
The qualification process for the expanded 48-team World Cup, to be held in the United States, Canada and Mexico, offers two extra places for South America with six teams qualifying directly.
The seventh out of the 10 nations will head to an inter-continental play-off.
After the opening two rounds Brazil lead Argentina on goal difference with Colombia third on four points, one ahead of Uruguay and Venezuela.
Paraguay, Peru and Chile have a point each.
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