PHOENIX -- Zack Greinke admitted to being a bit "amped up" in the first three innings of the Thursday night game, going as far as to apologize to the plate umpire for snapping at him.

Whatever the case, it didn't affect him much, as Greinke was nearly unhittable. The Diamondbacks ace came six outs away from his first no-hitter in 14 major league seasons, leading Arizona to a 2-1 win over the Pittsburgh Pirates.

Greinke (4-2) struck out 11, tying a season high, and walked one in eight innings. The only hit he allowed was Gregory Polanco's solo home run to lead off the eighth.

"Slider was really good, most pitches were really good," Greinke said. "It was a really good game for our defense, too."

Fernando Rodney, who hadn't pitched in six days, tossed a scoreless ninth inning for his ninth save in 11 chances this season.

Suspense for a Greinke no-hitter truly began to build when Andrew McCutchen flied out to deep center field to end the top of the seventh. Greinke walked to the dugout to cheers.

By then, Greinke had already started thinking he had possible no-hit stuff.

"First three (innings), just trying too hard, probably," Greinke said. "Last start was the best one the slider's been. Today was good, too. It felt better last start, but it felt great this start, too."

The crowd groaned with relief in the eighth as Polanco's deep fly ball down the right field line curved foul into the seats. But moments later, Polanco straightened out a Greinke slider, and it landed inside the pole for his first home run of the season.

"I said I have to keep fighting. I had to shorten my swing and get my hands closer to my body," Polanco said. "Try to stay inside the ball as much as I can, because all night he threw me inside."

Greinke's night was over after 107 pitches.

"I just felt at 107 pitches, it was time to turn it over to the bullpen," Diamondbacks manager Torey Lovullo said. "I had a number in mind. ... Once the no-hitter was lost, we wanted to make sure that we preserved the win and turned it over to the bullpen."

Lovullo said he would have allowed Greinke to go out for the ninth inning if the no-hitter had remained intact.

Pirates starter Gerrit Cole pitched well but got no run support once again. Pittsburgh's offense has scored a total of five runs in Cole's last five starts while Cole has been in the game, and his NL-low 2.09 run-support average dipped even lower after Thursday.

Cole (1-4) was the hard-luck losing pitcher though he allowed just two runs on seven hits in seven innings, striking out five with a walk. The Pirates (14-21) lost their fifth consecutive game.

"His effort out there was professional. He kept away from multiple-run innings," Pirates manager Clint Hurdle said. "He used all his pitches. He was efficient. He was effective. Early on, the fastball command was a little spotty."

Rodney, who often has had to work out of trouble for saves this season, got the first two outs before walking Josh Harrison. The game ended when Diamondbacks catcher Jeff Mathis, from his knees, threw out Harrison trying to steal second base with Francisco Cervelli at the plate.

The Pirates challenged the call, but it was upheld after a 2-minute, 14-second review.

"I just felt like that was the quickest way I was going to get it down there," Mathis said, admitting he doesn't throw from his knees much anymore at this stage of his career.

Chris Owings led off the bottom of the second inning with a double, then came home on Brandon Drury's single up the middle to give Arizona a 1-0 lead.

Drury has reached base safely in 30 of his last 31 games at Chase Field and has hit safely in nine straight games.

Peralta hit his second double of the game with one out in the third, then came home on Jake Lamb's double for a 2-0 lead. However, Cole was able to strand runners at second and third base by striking out Owings and Drury.

Diamondbacks right fielder David Peralta took a hit away from McCutchen to end the top of the first, diving to catch a sinking line drive.

A walk by Jordy Mercer in the third inning was the only baserunner Greinke allowed before Polanco's homer.

Mercer appeared to have his first stolen base of the season in the third, but he was called out upon replay review. The original safe call was overturned in a 39-second review.

The Diamondbacks (20-16) finished with seven hits.

NOTES: Pirates RHP Daniel Hudson returned to Chase Field for the first time since he won the 2016 season finale in relief for the Diamondbacks. Hudson, a popular player with teammates and fans, doffed his cap when introduced via public address before the top of the second inning. ... Pirates INF Adam Frazier (left hamstring strain) is 4-for-10 through three rehab games with Triple-A Indianapolis. ... Diamondbacks OF Yasmany Tomas got Thursday off, with Daniel Descalso starting in left field. Tomas, who homered on Wednesday, is hitting .352 (19-for-54) with seven doubles, four home runs and 19 RBIs in his past 14 home games. ... Arizona RHP Taijuan Walker was feeling ill before his last start on Sunday at Colorado, in which he took the loss. However, Walker is feeling fine, and any sickness that affected Diamondbacks players recently has worked its way out of the clubhouse, manager Torey Lovullo said. Walker isn't scheduled to pitch again until Saturday.