Mets rookie right-hander Zack Wheeler pitched a gem, with Hill's homer the only blemish during his 6 1/3 innings of work.
The right-hander mixed his mid-90s fastball with his offspeed stuff to keep the D-backs' hitters off balance throughout.
"I was just trying to throw strikes and get ahead of guys," said Wheeler, who improved to 5-2. "That was the main point tonight."
The D-backs managed just four hits off Wheeler through the first six innings.
Arizona starter Brandon McCarthy, who was making his second start since coming off the disabled list, kept the Mets mostly in check as he looked sharper than he did in his last start against the Red Sox.
McCarthy allowed a leadoff homer to Juan Lagares in the fourth, and later in the inning, he gave up a couple of two-out hits that helped give the Mets a 2-0 lead.
That was all New York could manage against McCarthy, who scattered six hits over his seven innings of work.
"McCarthy threw the ball good," Gibson said. "He threw the ball much better than he did last time. He kept his stamina. He did a good job."
Stamina was the key for McCarthy. Last time out against the Red Sox, he tired noticeably in the fifth. Saturday night, he relished the opportunity to push himself through seven innings.
"I needed to get past that wall," McCarthy said. "I felt pretty good. There were a few pitches there that I'd love to have back, but overall, I thought I did a good job commanding the ball and kind of moving it around."
After Hill's homer, the D-backs managed to chase Wheeler from the game and load the bases against Scott Rice with two outs.
The left-hander recovered to get Adam Eaton to ground out to end the threat, and New York still led, 2-1.
The Mets then gave themselves some breathing room in the eighth with a pair of runs off reliever David Hernandez, who was optioned to Triple-A Reno following the game.
Once again the D-backs loaded the bases with two outs in the eighth, but Gerardo Parra struck out against Pedro Feliciano to end the threat.
"They dodged some bullets tonight, that's for sure," Eaton said. "We just couldn't get that big hit. That's the story of the whole night. We had bases loaded a couple of times with two outs and couldn't come up with that big hit. Credit to their pitchers for keeping us off balance for most of the night and not allowing that big hit."
The offense has been an issue for the D-backs for a while now, but it appeared over their recent three-game winning streak the team was headed in the right direction.
The D-backs scored a total of 20 runs during the three-game stretch before coming up short Saturday.
"We have to come through," Eaton said. "It's our job to come through with that. That's what we need to do."
There's little doubt about that, but whether or not they do it is another story.