"That was a big lift for us," D-backs manager Kirk Gibson said.
The win helped the D-backs pull to within 3 1/2 games of the Dodgers and Giants, who are tied for first place in the National League West.
The D-backs grabbed a 3-0 lead in the first when Paul Goldschmidt hit a three-run homer off Aaron Harang.
The early runs were important, as the Dodgers came into the game having swept the Giants in a three-game weekend series and had momentum.
"You always want to get on top, these guys have been on a roll, so you want to jump on top of them," Gibson said.
Johnson, who was acquired Sunday from the last-place Astros, spent time before Monday's game introducing himself to his new teammates, learning the signs and trying to acclimate himself with a pennant race for the first time in his career.
"I told one of the guys this was like Opening Day for me," Johnson said. "My nerves were running wild tonight."
In his first at-bat of the game, Johnson flied out to end the first inning with a runner on first.
Then in the third, he came up with one out and the bases loaded and bounced into an inning-ending double play.
Possibly with that in mind, the Dodgers elected to intentionally walk Miguel Montero to load the bases to get to Johnson with two outs in the fifth.
"I had a chance early in the game to do something, drive some runs in and kind of let the guys down on that, too," Johnson said. "So not only was it the intentional walk, but that [earlier missed opportunity was] in my mind, too. I wanted to make up for that."
Boy did he ever, as he deposited a 2-1 offering over the wall in left for a 7-0 Arizona lead.
"Not that I was trying to hit a home run, but any time a guy gets walked in front of you on purpose you want to go up there and get a big hit," Johnson said. "I was just trying to square something up and got it up, and so got it out of the ballpark."
Harang's evening would end after the fifth, and he would spend the rest of the night lamenting the two pitches that wound up over the fence.
"You go back and look at it and it was two pitches," said Harang, who fell to 7-6. "The one to Goldschmidt, A.J. [Ellis] wanted a fastball down and away and it ran back middle. Obviously, it was a hanging slider to Johnson there in the fifth. I throw two different pitches and it's probably a different outcome and it might be the complete opposite and we are walking away with a victory."
Instead it was Johnson who was given the traditional postgame celebratory shower by his new mates. He was cold and wet when he met with the media, but could not have been happier.
"That's my plan," Johnson said. "I just want to contribute somehow. I know I'm not going to hit a grand slam every night, so if I can just do the little things, play some defense, run the bases, get some hits and just try to help these guys out."
Cahill (9-9) set the tone for the night when he worked out of a jam in the first inning. In his previous seven starts, Cahill had allowed at least one run in the first inning.
"We scored the runs, so you certainly don't want to let them back on the scoreboard," Gibson said of Cahill's scoreless first. "You want to shut them down there and continue to add on yourself. He made pitches when he had to make them tonight."