Heston (6-4) struck out 11 and did not allow a walk, but hit three batters -- including one in the ninth inning -- to ruin his chance at a perfect game. The three hit batters are the most ever in a no-hitter.
"Definitely something I'll remember forever," Heston said of the no-hitter.
The right-hander also helped his own cause by going 2-for-4 with two RBIs. He threw 110 pitches, with 72 counting as strikes and relied heavily on his sinker, throwing 66 of them on the night.
"Lot of emotions going through my mind right now," Heston said. "Hasn't sunk in yet. Looking forward to catching my breath and celebrating a little bit."
A 27-year-old rookie, Heston capped his career night with three straight strikeouts and is the first pitcher to end a no-hitter by striking out the side since Sandy Koufax in 1965, according to the Elias Sports Bureau.
"Attack the zone. Don't let the nerves get to me. Just throw quality strikes, and that didn't change in the ninth," Heston said of his approach. "Some extra nerves going on. Taking a little more deep breaths out there. I realized it and it was awesome to be part of it."
Heston called it the greatest moment of his life.
"This has got to be No. 1, probably right next to my first big league appearance," he said.
After freezing Ruben Tejada with a 91 mph sinker for the final out, Heston didn't jump, didn't raise his arms in triumph.
He hopped off the mound with two steps toward the Giants dugout, slapped his glove with his bare hand, then turned, walked toward home plate and hugged catcher Buster Posey.
"I wasn't too sure where to go after that last out," Heston said in an aw-shucks manner, looking boyish despite a day or two of stubble.
Heston's gem followed a rough 3 2/3-inning start against the Pirates. He is the first pitcher since Nolan Ryan in 1973 to throw a no-hitter after failing to complete four innings in his previous start, according to the Elias Sports Bureau.
"He had a really good sinker. And then he kept everybody off balance with a couple of different kinds of breaking balls -- two kinds of curveballs, one obviously slower, one a little quicker than a good slider," Mets outfielder Michael Cuddyer said. "But I think it was mainly his sinker. He had a lot of movement on his sinker. And he didn't make any mistakes. When he made mistakes, it hit a person -- three people. Those were really the only mistakes he made all night."
The Mets, who had not been no-hit at home since 1969, hadn't gone hitless in any game since 1993 -- the fourth-longest current streak behind the Chicago Cubs (1965), Oakland (1991) and Boston (1993), STATS said.
After plunking Anthony Recker with a pitch to start the ninth, the right-hander threw called third strikes past pinch hitter Danny Muno, Curtis Granderson and Tejada. Heston walked calmly off the mound toward home plate and was hugged by Posey.
"It's fun to see good things happen to good people," Posey said.
Heston is the first person to throw a no-hitter this season and the first Giant to toss one since Tim Lincecum last year.
The Giants, who have 17 no-hitters in franchise history, now have thrown four no-hitters in as many years as Matt Cain (2012) and Lincecum (2013, 2014) have done so in the past three seasons, with Cain's also being a perfect game. The only other team to throw a no-no in at least four straight years is the Los Angeles Dodgers, who did it from 1962 to 1965, according to STATS.
Heston made his big league debut last Sept. 13 against the Dodgers but this spring was sent to the minors on March 20.
"The numbers really got him more than anything," Giants manager Bruce Bochy said.
But when Cain started the season on the disabled list, Heston was brought up April 7. Before Tuesday, his only complete game was a two-hitter against Houston on May 12.
"Honestly, I think it's just a matter of him just kind of trying to find his way right now," Posey said after catching his third no-hitter. "He's still early in his career in establishing what type of pitcher he's going to be. And it's something that we all go through when we first get here."
When Heston returned to the Giants' clubhouse, he was met by one last ovation, this time from all his teammates.
"It was awesome, to walk in and having the whole team sitting there, congratulating me," he said. "Definitely a special moment. I'll remember that forever."
Information from The Associated Press was used in this report.