Diego Valdes finished off Julio Furch's feed three minutes before halftime, who had been on the back foot for much of the game before taking the lead.
Furch added a goal shortly after the break for Santos, coming off Javier Correa's pefectly weighted one-touch redirection of Brian Lozano's pass from the right.
The Red Bulls outshot Santos 14-10, led 5-4 in shots on target and took all seven of the match's corners, but were shut out at home for a second consecutive CCL game at home against a Liga MX opponent. Chivas drew the Red Bulls 0-0 in the second leg of last year's semifinals en route to winning the tournament.
The result means the Red Bulls must win either 2-0 next week in Mexico to force penalties, or by three or more goals to advance outright to get back to the semifinal stage.
Tuesday, March 12 at Santos Laguna, Leg 2, Concacaf Champions League quarterfinals (9 pm ET | UDN, YahooSports.com)