Barcelona have not lost any of their last 15 games against Atletico in LaLiga (11 wins and four draws).
Iniesta now has 10 days to recover before next week's Champions League second leg against Chelsea.
On 599 goals for club and country, the Argentine brought up the landmark in fitting style, bending a free-kick into the top corner midway through the first half despite a touch from goalkeeper Jan Oblak at full stretch.
However, Antoine Griezmann is in red-hot form for the visitors, after netting back-to-back hat-tricks in their last two games.
Atletico threw players forward in the final minutes of the game but could not find the equaliser as Barcelona walked away with the three points.
Thomas Partey fouled Messi 25 yards out with 25 minutes on the clock.
Luis Suarez thought he had scored a second after half-volleying through Oblak's legs but was flagged offside, before Jose Gimenez applied a crucial block to deflect a Messi shot over.
At the other end of the field, the referee also ruled out a goal by Gameiro for offside with five more minutes to go before stoppage time.
The only sour note for Barca was losing Andres Iniesta to an apparent hamstring strain in the opening period and, although Atletico improved after the break, Marc-Andre ter Stegen was barely tested, ensuring the day belonged to Messi and Barca.
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