With the score tied 1-1 late in the second half, Miller beat defender Kosuke Kimura to a crossing pass and launched a header that got past Red Bulls goalkeeper Luis Robles.
Jordan Harvey had earlier rallied the Whitecaps (4-4-4) from a 1-0 deficit with a tally in the 58th minute as Vancouver extended its unbeaten streak to four games.
New York (7-5-4) got its only score on an own-goal by the Whitecaps' Greg Klazura in the 51st minute.
New York suffered its first loss since April 7.
Swim Week Miami Beach 2014 [PHOTOS]