The game was halted by 2 hours, 7 minutes after four innings and when the contest resumed it turned into a battle of the bull pens.
New York relievers gave up three hits in five scoreless innings with Adam Warren earning the first major league win.
Warren (1-0), making the seventh appearance of his career, worked 1 2/3 innings in relief of CC Sabathia.
Sabathia gave up a first-inning run and did not return after the rain delay.
Stewart put the Yankees ahead 2-1 before the delay and Robinson Cano added a two-out, solo homer in the fifth after the game had resumed.
The loss went to Colorado starter Jeff Francis (1-3), who allowed two runs on four hits in four innings.
All three hits allowed by the New York relief corps came in the seventh, but the Yankees escaped the inning without giving up a run thanks to a double play and a strikeout of Todd Helton by David Robertson that ended the threat.
The win was the 499th as New York manager for Joe Girardi.