As the away side seemed on the brink of victory, New York defender Sands showcased his athleticism by soaring high to connect with a Santiago Rodriguez corner in the dying moments of stoppage time. With a powerful header, he sent the ball crashing into the net, leaving Herons goalkeeper Drake Callender with no chance.
The result puts a dent into Miami's hopes of beating New England's all-time single season points tally of 73 set in 2021.
The draw leaves Miami with 64 points from 30 games, meaning that Gerardo Martino's men must take nine points from a possible 12 remaining to equal the Revolution's record, or 10 from 12 to beat it.
Despite the late equalizer, Miami could have few complaints after New York grabbed a deserved point from Saturday's early fixture.
The hosts could easily have taken the lead earlier in the game only for poor finishing that let Miami off the hook.
Messi looked lively from the outset and almost opened the scoring with a fourth-minute free-kick from just outside the area that whistled past the post.
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However, New York continued to create the better chances and almost took the lead when Rodriguez's free-kick in the 11th minute rattled off the post and ricocheted off Miami goalkeeper Callender for a corner.
Keaton Parks missed a glorious chance to put New York ahead in the 47th minute, blazing well wide with the goal at his mercy in a huge let-off for Miami.
Miami looked to have made New York pay for their profligacy 15 minutes from time. Messi swept a pass out wide to Jordi Alba in space, and the former Barcelona man squared for Campana to tuck away a close-range finish.
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That goal against the run of play looked to have decided it, but after a late New York attack resulted in a corner, Rodriguez swung in a pinpoint cross from the set-piece to allow Sands to head home.
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(Except for the headline, this story has not been edited by staff and is published from a syndicated feed.)