Shortstop Jed Lowrie hit a two-run home run in the first inning, and catcher Chris Snyder clubbed a long three-run homer to left field in the second that put Happ in control with a 5-0 lead he wouldn't relinquish.
In addition to getting homers from players who weren't on the club last year, Houston drew a season-high eight walks, including three by Lowrie.
"That's my game, getting on base and having good at-bats," said Lowrie, who raised his on-base percentage to .410. "I'll take three walks any day of the week."
The win was the Astros' second straight over the Mets, giving them their first series win since taking two of three games from the Rockies at the start of the season. Houston will send ace Wandy Rodriguez to the mound Wednesday afternoon in search of its first sweep of the year.
The Astros have stressed getting on base at a higher clip with players like Jose Altuve and Jordan Schafer, and they've drawn 90 walks in 24 games after having only 56 free passes in their first 24 games of the 2011 season.
Altuve, J.D. Martinez, Matt Downs, Justin Maxwell and Snyder also drew walks, with Martinez driving in a run with a bases-loaded walk in the sixth. Altuve, hitting leadoff for the first time this year in place of the nicked-up Schafer, had his NL-best 13th multihit game of the season.
"We have some guys who are kind of growing up a little bit," Astros manager Brad Mills said. "You just get more experience and see things and look at other players and so forth and these guys are developing. I'd like to say it was everything we did in Spring Training, but that's not the case. These guys are doing a real good job of working hard and trying to get good pitches to hit, and that's important."
Happ, who meandered through a 6-15 season a year ago, delivered his fourth quality start in five outings by throwing 6 1/3 innings and allowing six hits and three runs while striking out seven. The team improved to 3-2 in games started by Happ (2-1), who's struck out 31 in 29 1/3 innings.
"Compared to last year, it's a good stretch," Happ said. "I feel good, and I felt probably better than the results maybe even tonight. I'm just trying to keep going with that as long as I can."
Lowrie followed up a hit by Altuve in the first with a two-run homer to left field, giving him three for the season.
"That Lowrie pitch, I regret throwing him a fastball there," said Mets starter Jonathon Niese, who lasted only three innings. "I wanted to throw him a curveball. I threw it up and in on him and he got it. And then the Snyder one, he just ambushed me first pitch and he got that one, too."
Consecutive singles by Brian Bogusevic (2-for-4) and Maxwell in the second set the table for Snyder, who hit a tape-measure shot onto the railroad tracks above left field for his first homer with the Astros, who took a 5-0 lead.
"I knew I got it," Snyder said. "It was right down the line, so definitely I was just checking to see if it would go fair or foul."
The bullpen backed Happ with 2 2/3 innings of scoreless relief, including 1 1/3 by Wilton Lopez. Brett Myers nailed down his sixth save in as many chances with an easy ninth. Opposing hitters are batting just .115 (3-for-26) with one walk against Myers this season.