Inter Miami dropped two points in the Major League Soccer Eastern Conference race after San Diego fought back twice to secure a 2-2 draw in Florida on Sunday.
The result leaves Miami 11 points behind leaders Nashville with eight regular-season matches remaining.
San Diego took a surprise lead after 12 minutes when Danish forward Anders Dreyer raced onto a through ball from compatriot Jeppe Tverskov and chipped Miami goalkeeper Dayne St. Clair.
Messi restored parity in the 24th minute with his 101st goal for Miami.
The Argentine curled a free-kick from the edge of the area through a crowded six-yard box, with the ball clipping the inside of the post before finding the net.
Miami dominated possession and territory for much of the game afterwards, with Messi, Luis Suarez and Rodrigo De Paul all coming close to putting the hosts ahead.
The pressure finally paid off in the 74th minute when De Paul picked out Suarez with a clever pass near the edge of the area, allowing the 39-year-old Uruguayan to fire Miami into a 2-1 lead.
However, San Diego refused to settle for defeat and levelled six minutes from time.
Tverskov again supplied Dreyer with a precise pass over the top, and the Denmark international calmly finished to complete his brace.
San Diego almost snatched all three points in stoppage time when Kieran Sargeant broke on the counter-attack, but St. Clair blocked his effort to preserve the draw.
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