Cespedes hit a go-ahead homer in the eighth inning moments after pinch-hitter Kelly Johnson connected for a tying shot, and the Mets rallied past the Nationals yet again for a 5-3 victory Wednesday night.
The three-game sweep extended New York's division lead to seven games over Washington with 23 to play. The Mets have won six straight against the Nationals, including a three-game sweep at Citi Field from July 31 to Aug. 2.
"This has been the biggest three games I've had in my career," New York manager Terry Collins said. "Exciting games. Every one of them was a great game. Just huge comebacks, big hits, inspirational play by every guy that was out there."
Johnson's leadoff drive against Strasburg tied it 2-all and quieted the crowd at Nationals Park. Cespedes teed off for a two-run shot against struggling Drew Storen, sending the Mets to their third consecutive comeback victory in the series.
"The whole team is clicking, ready to fight until the last out," Cespedes said through a translator. "We know we're going to come back."
Bryce Harper homered twice, doubled and scored three times for Washington, but it wasn't enough.
Last season's NL Rookie of the Year, deGrom (13-7) gave up two runs and five hits. He struck out nine and walked two.
"That was the goal when we came in here, to win all three of these, and that's what we ended up doing," deGrom said. "It's been a lot of fun."
Strasburg (8-7) was charged with three runs and five hits in 7 1-3 innings. He was pulled after Curtis Granderson's single, and Cespedes drove Storen's second pitch into New York's delirious bullpen in left-center for a 4-2 lead.
It was the 14th home run for Cespedes since the Mets acquired him from Detroit on July 31 and ruined a spectacular effort from Strasburg.
"I went out there and battled," Strasburg said. "I just made a bad pitch to Johnson. What are the chances? Fresh off the bench, and he takes me upper deck."
Storen was right in the middle of a meltdown by the Nationals' bullpen Tuesday night, when Washington squandered a six-run lead in an 8-7 defeat. The former closer gave up a three-run double to Cespedes and walked three straight batters, allowing the Mets to tie the game in a six-run seventh.
New York also rallied from behind Monday and beat the Nationals' bullpen after starter Max Scherzer left with the score tied at 5.
Jeurys Familia closed for his 39th save.
Travis d'Arnaud and Harper exchanged early solo homers before Clint Robinson gave Washington a 2-1 lead with an RBI single in the fourth.
NOT MUCH RELIEF
Washington's bullpen gave up 12 runs in the series. "I feel for those guys getting out there and giving up runs because they're not intending to, that's for sure," Nationals manager Matt Williams said.
Cespedes is hitting .308 with nine doubles, three triples and 36 RBIs since joining the Mets.
Mets: LF Michael Cuddyer (right wrist tendinitis) was scheduled to take some swings for the second straight day. Collins remained hopeful Cuddyer could return to the lineup Friday in Atlanta.
Nationals: The team is dealing with several ailments, as 3B Yunel Escobar (103-degree fever), CF Michael A. Taylor (swollen right knee) and 1B Ryan Zimmerman (left oblique soreness and tightness) were all out of the starting lineup. It was not known when they will return.
Mets: Bartolo Colon (13-11, 4.18 ERA) tries to extend his scoreless streak of 25 innings in Thursday's series opener against the Braves.
Nationals: Gio Gonzalez (10-7, 3.96) has fared well against the Marlins, going 6-3 with a 2.44 ERA in his career.