"It's always good for us, as a team, to be able to put a couple of runs together," said Gonzalez, who hit his 15th home run, his fourth in six games and 10th this month.
Gonzalez's homer came on a 0-1 pitch came off Charlie Manning (0-1) and snapped a 2-2 tie.
"We haven't been consistent this year in adding runs once we take a lead," said Gonzalez. "So for Kouz to get the home run against the righty was key for us to get a little cushion, so our pitchers will have a little more comfort and not feel like one pitch might tie the game."
Gonzalez, who won Sunday's 18-inning marathon against the Reds with a three-run walk-off home run, has 25 RBIs this month.
Kouzmanoff's homer, his eighth, came off Joel Hanrahan, who came on to relieve Manning. It was Kouzmanoff's fifth dinger in his last seven games and third in his last two.
The home runs made a winner out of Heath Bell (1-3), who relieved Bryan Corey with a runner on second and two outs in the seventh and got Felipe Lopez to fly out to center.
Bell pitched a scoreless eighth before Trevor Hoffman came on in the ninth to pick up his 10th save in 12 opportunities
San Diego starter Randy Wolf threw six innings and allowed two runs. Wolf gave up seven hits, including a two-run home run to Aaron Boone in the first inning, struck out five and walked none.
Washington starter Shawn Hill gave up five hits and walked five, which played into the Padres' two-run third inning.
Hill walked the bases loaded with two outs and ran the count to 3-2 on Michael Barrett, who lined a single to center, scoring both Gonzalez and Kouzmanoff. It was Barrett's second straight start since returning from the disabled list.
"I think when we started the season, we felt very comfortable with Michael and Josh Bard," said Padres manager Bud Black. "When Michael went down [with a sprained right elbow ligament], that was a big blow. We felt that the two would have done a good job for us. With Josh out, Michael will get the lion's share of work, and I think he's responding. He swung the bat well in the Minors [and] he had some good swings Sunday without much to show for it, but he came through tonight."
Black believed there was some carryover from the Padres' 12-9 win on Sunday.
"Winning on Sunday was, obviously, a big win going into the off-day," said Black. "That would have been tough to swallow, losing that game. The guys came into the game with a little bit better feeling after Sunday's win.
"Kouz is swinging the bat better," said Black. "He's getting the head out on some fastballs. And even the last three or four days it looks as though he's recognizing the breaking balls better. He has laid off a number of sliders down below the zone.
"If that's the case and he's hitting like he did last August and September, it's going to help the lineup, and especially the guys in front of him."