Messi, who had missed Wednesday's US Open Cup final defeat to Houston and last week's draw in the league at Orlando, was again missing with the injury which has troubled him since mid-September.
Without the Argentine and his former Barcelona teammate Jordi Alba, who is out with a hamstring injury, Miami looked short of ideas. After a lacklustre game, New York struck in the 77th minute with a fine individual goal from Santiago Rodriguez.
The Uruguayan brought down a long ball from Tayvon Gray and held off two Miami defenders as he turned before blasting into Drake Callender's near post.
Miami had not managed an effort on target in the entire 90 minutes but then in the fifth minute of stoppage time defender Tomas Aviles rose to head in a Robert Taylor corner.
The home side were desperately close to grabbing a dramatic late winner when David Ruiz burst into the box, but his drive from close range bounced out of the underside of the bar.
Miami are in 13th place in the East, four points behind ninth-placed Montreal, who occupy the final playoff spot, but with a game in hand on the Canadian team.
Miami head coach Gerardo Martino said that Messi has been training but separate from the team and that he was improving his fitness but remained a doubt for Wednesday's trip to Chicago.
"He is training on the field, different from the group but he is feeling better and better," said Martino.
"On Tuesday we will evaluate him because we make the trip to Chicago. But we are not going to take any kind of risk. If we interpret from the talk with the player and the doctors that the risk is still present, the player will be out of the game," he said.
"But I can't say today that he is out of the Chicago game because he is training better and better and there is nothing left to do but evaluate him day by day," he added.