Each team scored in the second half, meaning the Red Bulls continue their search for a first win of 2014.
The first half was controlled by the home side, but despite having the majority of possession, the Red Bulls were unable to trouble Rapids goalkeeper John Berner, who was filling in for the injured Clint Irwin.
New York opened the scoring in the 57th minute. Lloyd Sam floated a dangerous cross into the box and with both Rapids center backs occupied, Thierry Henry was on hand to open his 2014 account with a diving header.
The lead would only last 15 minutes, however. Jamison Olave bumped Marvin Chavez over in the box, which prompted the referee to point to the spot. Sanchez buried the penalty, despite Luis Robles guessing the right way.
The Red Bulls pushed for a late winner, but it wasn't in the cards, and the defending Supporters' Shield winners have now started the season 0-1-1. The Rapids begin their season with a credible road point.