The victory means Cincinnati (2-1-0, 6 points in the tourney) will finish second in Group E. The Red Bulls (1-2-0, 3 points) took a huge blow, as they aren't currently one of the four third-place teams that would advance due to their minus-3 goal differential.
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Cincinnati notched their second goal of the night on a Red Bulls own goal off a 56th-minute corner kick, to help them to a second win of the tournament.
The Red Bulls outshot FC Cincinnati 19-4 but only put four on target. Cincy goalkeeper Przemyslaw Tyton had four saves, but didn't make his first stop until the 81st minute.
Kubo's goal was set up by a miscue in the 43rd minute as New York defender Amro Tarek failed on a clearance attempt and left the ball alone near the box.
Kubo pounced on the mistake and rushed in to slam a right-footed shot to the left of Red Bulls goalkeeper David Jensen to give Cincinnati the lead.
The goal was just one of two Cincinnati shots in the first half. Both were on target -- their only shots on goal all match -- while New York was off-target on all five of its first-half attempts.
Cincinnati had an opportunity to increase the lead in the 52nd minute, but forward Adrien Regattin sent a left-footed shot wide left of the net.
But the club wasn't dismayed, and midfielder Haris Medunjanin lined up for a corner kick four minutes later. Medunjanin's kick toward the net glanced off the head of Red Bulls midfielder Florian Valot and slightly changed directions, stunning Jensen as the ball caromed off his arms and into the net.
Jensen made one save for the Red Bulls.
FC Cincinnati advance to knockout round of MLS is Back Tournament
Jaap Stam's squad shuts out New York Red Bulls 2-0 to go to the knockout round. Watch MLS on ESPN+.