The Diamondbacks got some help, though, when Clayton Kershaw pitched the Dodgers to a 2-1 victory over San Francisco in Los Angeles. Any combination of three Arizona victories or San Francisco losses and the Diamondbacks will dethrone the Giants as division champions.
"It's not like we're trying to make outs. We're up there trying to get base hits and push runs across," Bloomquist said. "The bottom line is at the end of the day we're still in a pretty good position. I'd rather be in this position than the other guy's position. People just need to relax a little bit. We know what we're doing. We're playing hard. We're going to be fine."
Morton (10-10), loser of his previous four starts, allowed three hits and struck out five in his first victory since Aug. 8.
Daniel Hudson (16-11) lasted five innings for the Diamondbacks, allowing three runs and seven hits.
The Diamondbacks, 1-0 winners on Monday night to give Ian Kennedy his 20th victory, close out their three-game series with Pittsburgh on Wednesday, then have Thursday off before hosting the Giants in a three-game set beginning Friday night.
"I don't think about when we're going to clinch," Diamondbacks manager Kirk Gibson said. "I know we just keep pushing ahead game by game and try to play a good game, pitch good, execute better at the plate and I believe that things will take care of themselves. I'm not thinking about any celebrations at all. Trust me."
Arizona has lost four of six.
Still, Gibson said, "We're what, 5½ up with seven to go? That's a pretty good position to be in."
After Morton was lifted for a pinch-hitter in the seventh, the Diamondbacks' Gerardo Parra and pinch-hitter Sean Burroughs singled off reliever Chris Leroux. Jason Grilli came on and gave up an RBI single to Bloomquist, but retired the heart of the Arizona order when Aaron Hill flied out to center, Justin Upton bounced out to second and Miguel Montero flied out to left.
The Pirates got that run back and more when usually reliable setup man David Hernandez faltered. Presley led off with his second double of the game then with two outs Lee slammed an 0-1 pitch over the wall in left for his sixth home run of the season.
Arizona restored the two-run margin with two runs in the eighth. Chris Young doubled and Ryan Roberts singled him in. With runners at first and third and two outs, Bloomquist put down a bunt that the third baseman Alvarez -- who had made two sparkling plays earlier -- threw wild to first allowing a run to score and make it 5-3.
Joel Hanrahan pitched a perfect ninth for his 39th save in 42 tries.
Doubles by Presley and Neil Walker to start the game put Pittsburgh up 1-0, then Alvarez's towering first-pitch homer to right made it 2-0 in the second.
Hudson walked the first two batters he faced in the fifth, then Ryan Doumit followed with an RBI double to put the Pirates ahead 3-0. Hudson walked Alvarez intentionally to load the bases, then got Ronny Cedeno to pop out to escape further damage.
Spectacular catches by Presley in left and Garrett Jones in right saved at least a run in the Arizona first. Presley ran down Upton's drive to deep left-center and Jones' diving grab robbed Paul Goldschmidt to end the inning.
"Both teams left a large amount of people on base but we did play excellent defense," Pittsburgh manager Clint Hurdle said. "A number of different times, the two catches in the first inning jumps out plus Presley goes in the gap to get one, Pedro had a couple. We were good in the field and Charlie pitched a solid ball game."
Singles by Montero and Young, followed by a wild pitch, put runners at second and third for the Diamondbacks with one out in the fourth. Morton fanned Roberts, then walked Parra intentionally to load the bases for Hudson, a .274 hitter. But the Arizona starter's harmless bouncer to second on the first pitch ended the threat.
Pittsburgh had 14 hits, eight for extra bases, and stranded 12 runners while snapping a four-game losing streak.
Diamondbacks President and CEO Derrick Hall, who announced Tuesday he has prostate cancer, sat in his usual seat near the dugout and got hugs of support from several red-clad team employees. ... Morton had two hits all season -- in 48 at-bats -- before his single and double on Tuesday night. ... Left-hander Wade Miley (3-2, 4.24 ERA) makes his seventh major-league start for Arizona on Wednesday. Right-hander Ross Ohlendorf (1-2, 6.82 ERA) goes for the Pirates. ... Pittsburgh had two runners picked off.