Lo Celso, in his first World Cup start, put Argentina ahead with a direct free kick in the 19th minute in Arlington, Texas, on Saturday night (Sunday AEST).
Messi added one of his own after entering the game in the second half, and the top scorer in World Cup history extended his mark to 19 goals.
Messi, the tournament's leading marksman with six goals, was among nine Argentina starters changed from the previous game, with Group J already clinched before the match.
He entered in the 60th minute, three days after his 39th birthday, and in the same stadium where he broke the scoring mark last Monday, and scored in the 80th minute.
Their captain had scored all five of Argentina's goals in wins over Algeria and Austria, including his first-ever World Cup hat-trick and then two goals in his record-setting game on Monday.
Messi has scored in seven consecutive World Cup games, breaking a tie with France's Just Fontaine and Brazil great Jairzinho for the longest all-time streak.
Lautaro Martinez put Argentina up 2-0 when he scored with a penalty kick in the 31st minute.
Martinez, who was subbed out for Messi, and goalkeeper Emiliano Martinez were the only players to start all three of Argentina's group matches.
Argentina, with seven wins and two draws in their past nine World Cup games, play in the round of 32 on Friday against Cape Verde. That game is in Miami, the home of Messi's Major League Soccer team.
This is the fifth time Argentina has won all of their matches in the group stage, and first since back-to-back tournaments in 2010 and 2014. Argentina have 14 wins, two losses and three draws in their past 19 group games.
France and Mexico were the only other squads in this expanded 48-team World Cup to get the maximum nine points in the group stage.
Jordan, the world's 72nd-ranked team, lost all three games in their first appearance in the tournament, and were outscored 8-3.
Mousa Altamari, who entered the game at the start of the second half, scored in the 55th minute for Jordan.
Lo Celso and Martinez both scored their first World Cup goals.
Only a couple of minutes after Lo Celso was offside when he kicked the ball into the net, he received a free kick after being tripped just outside the penalty box by Mohannad Abutaha, who drew a yellow card.
It was the first direct free kick for an Argentina goal in a World Cup since Messi against Nigeria in 2014.
After Martinez shot off the crossbar, Julian Alvarez followed with a header that was deflected by keeper Yazeed Abulaila over the net. But a VAR replay showed Alvarez took a kick to the face on the play, setting up the penalty.
