Trailing 4-2 in the fifth inning, the Rockies tallied three times to grab the lead.
After loading the bases with two out, Mets starter Dillon Gee (0-3) forced in a run with a walk issued to Michael Cuddyer.
Helton followed by lining a 1-1 pitch up the middle to chase home a pair for the lead.
Eric Young went 3-for-5 with two RBI and Carlos Gonzalez homered for the Rockies, who persevered through cold weather to take the opener of a four-game series.
The game had been rescheduled from Monday after heavy snow in Denver.
Juan Nicasio (2-0) went five full innings to earn the decision despite yielding four runs on six hits.
Gee ended up allowing five runs on seven hits over 4 2/3 frames.
David Wright went 3-for-4 with two homers and three RBI for New York.
Celebrity Families of 2014 [PHOTOS]