The Yankees scored six runs in the eighth inning to put the game on ice as they beat the D-backs, 9-3.
"We couldn't end the inning in the eighth," Arizona manager A.J. Hinch said.
The bullpen, which has been a sore spot for the D-backs all season long, has a Major League-worst 7.15 ERA. On Tuesday, it was a combination of Esmerling Vasquez and former closer Chad Qualls who struggled.
Vasquez did not retire any of the five batters he faced, allowing four hits and a walk, while Qualls gave up an RBI single and a two-run double.
Given the bullpen's history this year, it begged the question of whether Hinch should have stayed one inning more with starter Dan Haren, who had 109 pitches through seven. There are limits to what a starting pitcher can be expected to provide, however, and Hinch knows he has pushed his starters more than most, particularly Haren.
"We can't continue to ride him too heavy," Hinch said. "It's easy to want to do that. It's easy to want to leave him in. we've taxed him pretty much every start. He hasn't had a breather."
Haren had thrown 114 pitches in each of his past three starts, and in his outing before that stretch, he threw a career-high 126 pitches.
"It's a little dangerous going out there with 110 pitches and getting the top of the lineup," Haren said. "I think [Hinch] felt more comfortable going to the bullpen. I maybe could have gone back out there, but our starting pitching has been pushed quite a bit, so I don't think my going back out there would have been smart."
Haren (7-6) found himself in an early hole when Derek Jeter led off the game with a single to center and two outs later, Alex Rodriguez hit a 1-1 pitch into the bleachers in left for a 2-0 New York lead.
"I made that one pitch trying to go inside and left it out and over the plate, and he just got enough of it," Haren said. "That's a very good lineup, obviously, so any mistake you make, they will probably make you pay."
It was the first homer for Rodriguez since June 3, a span of 49 at-bats.
"He's a guy that strikes a lot of guys out," Rodriguez said of Haren. "He has a good split-finger [fastball], and that's the pitch you definitely don't want to chase. He makes his living with that pitch and opposing hitters chasing. Our philosophy as a team was to let him get the ball up."
The Yankees were able to get to Haren for one more run in the third, when with two outs and a full count, Nick Swisher managed a single to center. Mark Teixeira and Rodriguez followed suit, with Rodriguez's knock scoring Swisher to give the Yankees a 3-2 lead.
"I had two outs and two strikes, and they end up scoring a run, so that was kind of disappointing," Haren said. "The second hit A-Rod got off me was really the game, but they busted it wide open [in the eighth]."
Not only did he limit the Yankees' damage through seven, but Haren accounted for both of Arizona's runs in the second when he grounded a two-out, two-run single down the right-field line.
It was one of two hits for Haren on the night, as he raised his batting average on the season to .452 with six doubles and six RBIs. In 42 at-bats, he has struck out just five times.
"I do everything I can up there -- I try to put together the best at-bat I can and try to make the pitcher work, and good things have happened because of that," said Haren, who now has his second six-game hitting streak of the year. "Basically, I'm trying not to strike out. I've done a good job of not striking out this year. I've put the ball in play, and it seems like ground balls have gone through, so I'll just stick to that plan."