The loss, combined with the Dodgers' win over the A's, resulted in the D-backs falling out of first place and into second, one-half game back in the National League West.
Arizona trails Atlanta by a half-game for the NL's second Wild Card spot.
"For me, August and September baseball is all timing and rhythm and the hot team is going to start to carry some things within the division," D-backs manager Torey Lovullo said. "Hopefully that's us. I think we've got a lot of potential to do it."
Following through on doing so is another story. So far this year, the D-backs have not been able to get on a run like they did at points last year when the captured the top Wild Card spot.
This year, their longest winning streak is just five games.
After rallying with a two-run ninth to win in 14 innings Monday, Lovullo said he hoped it would be a "push win" for his team that would help start a win streak.
Instead, the D-backs struggled to score against right-hander Nick Pivetta (7-9) as he allowed just five hits over six innings.
"I'm confident with our guys," Lovullo said. "I know that we've had grinding days and grinding weeks and grinding months offensively. Yes, sometimes I can chalk that up to really good pitching and other times I feel like we haven't been executing the way that we're capable of executing."
Greinke (12-7) looked shaky early as he uncharacteristically struggled with his command, walking four of the first 10 batters he faced.
"A little wild early and then I got better as the game went on," Greinke said. "I felt good the whole time, just wasn't hitting my spots early."
The veteran, though, was able to keep the Phillies off the scoreboard over that span and the only damage they were able to inflict against him was a homer by Nick Williams to open the third.
"Greinke is an amazing pitcher," Pivetta said. "He's a top-tier starting pitcher. He's a No. 1. He's always been there, so you really have to be perfect when you're facing a guy like that. But our guys chipped away. Nick Williams got us ahead really early and that was awesome, just having that one-run lead really boosted my confidence and the team's confidence."
Greinke said because he felt good physically, he didn't mess with his mechanics and instead just kept doing what he was doing.
"I kept trying and it got better," Greinke said.
The Phillies managed to tack on four runs in the eighth off the D-backs' bullpen to give them more than enough insurance runs.
MOMENTS THAT MATTERED Deja vu … no: Trailing, 5-0, entering the eighth, four of the first five D-backs hitters reached base and they pushed across a pair of runs and loaded the bases with one out. It brought back memories of Monday's dramatic comeback. This time, though, Eduardo Escobar grounded into an inning-ending double play as Arizona managed just two runs.
"You got that same feeling that something special was going to happen," Lovullo said. "And then you get the big double play ball unfortunately to end the inning."
WORK IN PROGRESS Lovullo is still trying to figure out how best to use his new bullpen arms. Left-hander Jake Diekman, who was acquired from the Rangers last week, struggled in the eighth, allowing four runs, only two earned as a result of his throwing error, and retired just one batter.
"The new guys are going to continue to get the baseballs and get opportunities," Lovullo said referring to Diekman, Brad Ziegler and Matt Andriese. "I'm not going to run from them. We're going to need them down the stretch."
YOU GOTTA SEE THIS Diekman's error started the eighth off on a sour note. Cesar Hernandez bunted and Diekman picked up the ball and skipped it past Paul Goldschmidt at first. Right fielder Steven Souza Jr. tracked the ball down and overthrew third base trying to nail Hernandez, who was able to trot home after ball wound up in the stands.
"Things broke down on us in the eighth inning," Lovullo said. "I know it wasn't pristine. We play a good brand of baseball here and we're going to address some of those concerns and make sure we don't do it again. You don't see it here very often and I'm proud of that."
UP NEXT The D-backs wrap up the three-game series with the Phillies and an eight-game homestand Wednesday afternoon at Chase Field. Patrick Corbin (8-4, 3.31 ERA) will start for the D-backs, and he comes in with a 2-1 record and 2.98 ERA over his last eight starts. The Phillies will counter with Vince Velasquez (8-8, 3.80). First pitch is set for 12:40 p.m. MST.