It was Barlow's third goal of the season and came after Cristian Espinoza found the net in the 80th minute for the Earthquakes (3-2-2, 11 points). San Jose has earned four points over its last three matches.
The two teams battled to a scoreless tie at halftime, as the Red Bulls (1-2-4, seven points) outshot the visiting squad 8-4 in the first half, but neither side could manage more than one shot on target.
Espinoza's marker, his fourth of the season, came on a left-footed shot from the middle of the box, by way of a Carlos Gruezo through ball. The Quakes were looking for their first road victory of the season.
New York had each of the first three tries of the contest, as Cory Burke and Dante Vanzeir pushed shots wide in the fifth and sixth minutes, respectively. San Jose goalkeeper JT Marcinkowski also turned aside a header from Dylan Nealis from the center of the box in the 14th minute.
Paul Marie and Carlos Akapo both had shots blocked in the initial 45 minutes for the Earthquakes, whose other two shots came in short succession in the 43rd minute. Jamiro Monteiro's shot was saved, and Jackson Yueill's struck the bar.
After that, Kyle Duncan and Burke both had off-target shots for the Red Bulls before halftime.
New York was limited offensively in the second frame until Barlow scored from close-range.
The Red Bulls play the second half of their two-game homestand when they host Houston next Saturday. San Jose will host Sporting KC the same day.