Following a scoreless opening period with little in the way of scoring opportunities, the Red Bulls broke the deadlock in the 57th minute when Thierry Henry capped a fine move down the left flank by turning in Roy Miller's square pass with a right-footed shot.
The hosts doubled their advantage 10 minutes later when Eric Alexander's cross was nodded home by Lloyd Sam, and it proved to be a pivotal goal as the Union cut the deficit in half with 10 minutes to play.
Sekagya was sent off for his denial of a clear scoring opportunity, reducing the Red Bulls to 10 men.
The Union, though, were unable to take advantage of the extra man in the closing stages of the match as they suffered their second defeat of the season.
New York (1-2-4) improves to seven points on the season, bringing the club level with the Union (1-2-4) in the Eastern Conference table.
The Union, winless in their last five outings, have yet to record a victory at Red Bull Arena.