Real Madrid remain two points behind Barca at the top of the table after Cristiano Ronaldo became the club's all-time leading scorer in La Liga with five goals in a 6-0 rout of Espanyol.
Messi started on the sidelines having missed training on Friday to attend the birth, a day after returning from Argentina international duty.
However, he was still to make the decisive contribution as he nonchalantly flicked home the winner 11 minutes from time after Neymar had cancelled out Fernando Torres's opener.
"I am happy to win the game and principally to score the goal. It was important to equalise quickly."
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Atletico boss Diego Simeone lamented his side's overall performance, but wasn't surprised to see his compatriot once again make the difference.
"Messi was the difference when he was on the pitch," said Simeone.
"He is a player that is used to turning the game and he did it once more today."
Even without Messi, Barca were the dominant side early on at the Calderon with Ivan Rakitic forcing Jan Oblak into the first serious save of the game with a fierce drive from a narrow angle.
Barca suffered a blow when Thomas Vermaelen was forced off with a calf injury.
Yet, Luis Suarez should still have given them a half-time lead when he turned Rafinha's flick onto the crossbar from point-blank range.
Atletico struck first six minutes after the break when Torres latched onto Tiago's through ball and his shot found the net via the far post.
However, the lead lasted barely three minutes as in the absence of Messi, Neymar was given the chance to strike a free-kick from the edge of the area and arrowed the ball into Oblak's top right-hand corner.