NEW YORK -- The D-backs got off to a fast start on Tuesday night in the Bronx, scoring in the first inning for the first time since July 22. After they tacked on that first run, Taylor Clarke went to work, leading the team to a 4-2 victory with a strong undercurrent of pitching -- and changes, too.

Clarke, in his first start back from paternity leave and 12th of his career, allowed one run over 5 1/3 innings. In the eighth and ninth, Archie Bradley recorded the final four outs to get his first save of the season.

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Bradley's appearance in a save situation came two days after manager Torey Lovullo said Greg Holland would be getting a breather from the closer's role after back-to-back shaky outings.

That isn't the only air of change surrounding the D-backs, who have been rumored to be having discussions about trading at least one of their starters. Heading into Wednesday's Trade Deadline (1 p.m. MST), Clarke's presence and success Tuesday could prove even more important. If the D-backs were to move a pitcher, they'd need to have others to rely on, and Clarke showed that he can help fill that void. It was his fourth outing of more than five innings and second straight such start.

The run he allowed in the sixth inning was unearned -- Aaron Judge came around to score after reaching on an Adam Jones fielding error to start the inning. Aside from that, Clarke was mostly untouchable, allowing three hits and walking two over a 95-pitch outing.

"He did a great job," Lovullo said. "Really did a good job of making pitches, duplicating pitches, finishing off hitters. ... This team, after a tough night of baseball [in Miami on Monday] and a tough travel night, showed its resiliency and its toughness. This is what we're all about. A game like tonight where the guys really dug in and reached back as far as they possibly could to beat a really, really good baseball team."

Clarke's start followed an outing of six innings and two runs against the Orioles last Wednesday. It's the first time he's gone five-plus innings in back-to-back starts since May 7 and May 25, when he did so with a trip to the Minors sandwiched in between.

"[I] kind of just took the momentum from last time and tried to repeat the same thing mechanically, stick with that game plan, getting ahead," said Clarke, who was supported by home runs from Christian Walker and Carson Kelly.

Fastball location was huge for Clarke, and he noted that "[in] my good games, I'm locating my fastball well and everything kind of plays off of that. So to be able to get that going was huge from the start."

Judge, who also struck out and walked against Clarke, corroborated that.

"He made pitches when he had to," Judge said. "I know he missed quite a few pitches in the zone that I think we could've done some damage on, but he was able to put it where he wanted to the majority of the night, and he did his job. We were able to capitalize on a couple of pitches, and you've just got to tip your cap sometimes."

After Clarke's night was complete, Lovullo lined up the bullpen to get to Bradley for the save.

"I just felt like I was matching up the best way that I could," Lovullo said. "I drilled down to Archie as closing it out, at that point in the game against that part of the order, and I wanted to match up the best I could prior to that. Those types of things work themselves out. The players and pitchers did their job. They threw the baseball where they wanted to and did what they had to do, the way they needed to do it."

Does this mean Bradley is now the D-backs' closer? Not so simple.

"I don't know," Lovullo said. "I don't know right now what I'm thinking. I spent a lot of time digesting the numbers and the matchups and I love what I've seen from Archie so far in that situation. It was a four-out save, it was a pretty special time for him. If I have to say, would I go to Archie again? Absolutely. But I want to make sure that it's a good matchup for him. We've got some very capable left-handed guys down in the bullpen, and if it's a better matchup for a lefty, I might do what we did toward the end of last year and get some outs with a left-hander as well."

Holding the Yankees to just two runs is no small feat. It's just the 15th time a team has held them to two or fewer runs this season, the fewest for any offense in baseball.

"We pitched, and we threw the ball where we wanted to, and we executed up on the mound," Lovullo said.