Ariel Lassiter drew the Herons level a second time and Pozuelo, acquired by on July 7th, won it with seven minutes left on the clock.
The result saw the Boys In Blue drop to third in the Eastern Conference while the Herons are level with New England and Cincinnati for the final playoff spot in the East.
Story of the match
Miami had their first chance ten minutes in as a fierce drive from Robert Taylor forced Sean Johnson to parry away with his hand.
There weren't many opportunities, but in the 28th minute, Rodriguez went on a deep run and shot from a narrow angle, unlucky to hit the left post.
Six minutes later, the Boys In Blue jumped in front. Moralez clipped a ball to the back post for Chanot, who headed back for Magno and his low drive hit the post and found the back of the net.
The lead didn't last long as Bryce Duke found Pozuelo and the former MLS MVP curled past Johnson to equalize.
After Nicolas Acevedo volleyed just past the left post, Moralez sent in a lovely pass started the next passage of play that ended when Callender saved a shot by Rodriguez, but Andrade was on hand to convert the rebound.
On 52 minutes, Pereira was forced off through injury to be replaced by Heber.
Johnson saved from Jean Mota, but Lassiter equalized shortly after that to make it 2-2 in the 63rd minute.
With a little more than 20 minutes to play, Higuain was denied by Johnson after being spotted in the six-yard box.
The Boys In Blue made their final substitution in the 74th minute with Justin Haak coming on for Andrade.
Another substitute Malte Amundsen thought he had won a penalty after being fouled by Damion Lowe, but referee Drew Fischer instead signalled for a goal kick.
With seven minutes remaining, the Herons found a winner as Pozuelo pounced on a loose pass by Alfredo Morales to finish past Johnson.
Man of the match: Alejandro Pozuelo
His first two goals were critical and his presence alone seems to have revaitalized Higuain. With three assists and completing passes at almost 90 percent, the Spaniard is already proving to be the difference-maker Miami thought he would be.