Jackson (7-8) had allowed only a triple to Mike Baxter in the first inning and set a season high with 10 strikeouts through six. But in the seventh, the right-hander issued a leadoff walk to David Wright and Davis drove the next pitch the other way to left field for his 22nd home run.
Seventeen of his 22 homers have come on the road, most in the NL.
"I wasn't trying to go anywhere. I was just trying to hit the ball," Davis said.
"We didn't really do a great job of that tonight, partly because (Jackson) was so nasty. But he left a fastball up and away and I hit it on the barrel and it got out of there."
"Oh, man. He was nasty tonight. He had everything. He was throwing all his pitches for strikes. His fastball was moving everywhere and his slider was real sharp," Davis said.
After allowing a leadoff single to Espinosa in the sixth, Niese retired the last seven batters he faced.
"It was one of those nights where everything felt good," he said.
Francisco was helped by Baxter, who made a nice running catch of Zimmerman's fly ball to right to start the ninth.
"It was a good catch. I really had no idea why he was there, but he got me out," Zimmerman said.
Niese, who is 3-0 with a 2.37 ERA in six games against Washington, allowed five hits and struck out seven without a walk.
"It seems like when you need him most, he steps up," Mets manager Terry Collins said. "Tonight he knew we needed him again and he gave us a great outing."
New York posted its 11th shutout of the season, while Washington was blanked for the fifth time.
Jackson pitched seven innings, allowing two runs and two hits. He walked one and struck out 11.
"Tonight, Niese was the better pitcher. He held us scoreless. The bullpen did the same. I gave up two runs. I lost," Jackson said.
Washington manager Davey Johnson was impressed, though.
"That was probably the most dominant I've seen him pitch," Johnson said. "He was fun watching. His stuff was so electric. He was overmatching them."
It was only New York's fourth win in 14 games against the NL East leaders this season.
"It's great to beat them. You always want to beat the best. And right now they're the best in the division," Davis said.
The Nationals remained four games ahead of second-place Atlanta, which lost to the Los Angeles Dodgers. The two teams begin a three-game series Monday in Washington.
Collins said he would meet with general manager Sandy Alderson on Monday to discuss struggling LHP Johan Santana. Collins said Santana is scheduled to pitch Thursday. The 33-year-old left-hander, who missed last season following major shoulder surgery, permitted six runs and seven hits over five innings Friday in his second outing since spending three weeks on the disabled list with a sprained ankle. He has lost five straight starts, giving up at least six runs in each one. Collins said Santana wasn't asking to be shut down. "I don't think he's asking for it. What he's basically saying is if that's what we think we should do to make sure he's healthy next year, he's on board with that," Collins said. ... Johnson said he would give SS Ian Desmond the day off on Sunday. Desmond returned Friday from more than three weeks on the disabled list with a strained oblique muscle. ... For the 500th straight time, the character portraying Teddy Roosevelt lost in the Nationals' "Racing Presidents" mascot race. ... The crowd of 42,662 was the second-largest in Nationals Park history. ... Washington LHP Gio Gonzalez (15-6, 3.29 ERA) pitches Sunday against New York RHP Jeremy Hefner (2-4, 4.76).