The hosts started brightly with a series of set pieces. The best opportunity fell to Chance Myers, who could not hit the target from the edge of the box.
Peterson Joseph then had a couple of efforts saved for the home side before, against the run of play, the Red Bulls took the lead.
A counter-attack saw Dax McCarty break from midfield and play an excellent through-ball to Steele, who finished confidently into the bottom corner.
Kansas pushed forward after that with Kei Kamara getting more and more involved until he eventually scored, smashing the ball into the roof of the net from close range.
Midway through the second half, though, the visitors went back in front. Sam found Espindola just inside the box and the attacker fired past the goalkeeper into the far corner.
Sam got on the scoresheet himself five minutes later, finishing well after another quick counter-attack.
Kamara and Myers both missed half-chances as the game wore on before Soony Saad headed against the crossbar.
Dominic Dwyer pulled a goal back for the hosts in the final minute, but it didn't matter as New York held on for an important win.