Defender John Tolkin added the second goal of his MLS career in the 15th minute for the Red Bulls (11-8-7, 40 points), who snapped a two-match scoreless and three-match winless run while solidifying their fourth-place position in the Eastern Conference.
The Red Bulls allowed Atlanta 73.2% of the possession but were the more dangerous side throughout their eighth away win of the season -- tied for the most in MLS.
Josef Martinez scored for Atlanta late in second-half stoppage time, preventing his team from being shut out at home for the third time this season.
Rocco Rios Novo made three saves for Atlanta (7-10-8, 29 points), which remained in 13th place in the East and saw a modest three-match unbeaten run halted.
The Red Bulls are one of MLS' most transition-oriented teams, but their opening goal came from a spell of relatively innocent looking possessions.
Right back Kyle Duncan had the ball near midfield, pushed forward down the right flank, eventually beat his defender and then sent in a low cross into the penalty area.
Cristian Casseres Jr. took a subtle touch to redirect it into the path of Morgan near the penalty spot, and Morgan hammered a low, first-time finish past Rios Novo into the bottom left corner.
Tolkin made it 2-0 four minutes later. After a short corner, he tried to spot forward Patryk Klimala inside the penalty area.
The intended pass was just too high for the forward's head, but with Rios Novo anticipating a redirection, the ball skipped off the turf and inside the left post with the goalkeeper rooted to the ground.
Klimala was originally ruled offside, but the goal was given following a video review that showed he was kept on by the foot of an Atlanta defender.
Martinez's sixth goal of the season, set up by Luiz Araujo, gave Atlanta brief late hope, but the final whistle came only moments later.