Todd Frazier finally won it for them with his bat.
Frazier's two-run homer in the 15th inning lifted the Reds past the Nationals 4-3.
"I [wanted] to drive something. I had two good at-bats before that. It's crazy how the game goes," Frazier said. "You're 0 for 3 and then you get three more at-bats in extra innings and you go 3 for 3. So it's like a whole new game and I got a ball up, elevated and tried to drive it."
The Reds twice made two-out diving catches that prevented the winning run from scoring.
Phillips robbed Wilson Ramos behind second base with a runner on third to end the 11th.
"I knew if I was going to get it, I had to go right away," Hamilton said. "If I hesitated one little step, it would have been down."
"That was just a total grind, every player on the team played some sort of role in that game, and the defense was phenomenal," Reds manager Bryan Price said.
Frazier's home run also ended a 27 2/3 innings scoreless streak by the Nationals' bullpen.
"Bad execution, bad pitch selection, pretty much bad all the way around," Detwiler said.
Washington trailed 2-1 when Espinosa doubled to left off Aroldis Chapman to start the ninth. He advanced to third on a fly to deep left-center by Kevin Frandsen and scored on pinch-hitter Scott Hairston's fly to deep left.
That rally cost Reds starter Mike Leake his first victory since April 15.
Monday night was the first meeting between Leake and Stephen Strasburg, youth league teammates in San Diego and 2009 first-round draft choices, with Strasburg going first overall and Leake eighth.
Leake, who left with a 2-1 lead, saw the bullpen blow its third save in games he has left with the lead. He gave up a run and seven hits, and is 0-1 with 1.82 ERA in four starts in May.
Strasburg went seven innings, allowing two runs and six hits. He walked only one, but hit two batters, both of whom scored.
Both teams had their share of chances. The Reds were 2 for 24 with runners in scoring position, and the Nationals were 2 for 18.
"All you can do is hit and sometimes you wish you could steer it after you hit it, but that doesn't happen," Nationals manager Matt Williams said.
The Reds were without first baseman Joey Votto (strained left quadriceps), who is rehabbing in Cincinnati, for the fourth consecutive game.
Trailing 2-0, Washington finally got to Leake in the seventh. Nate McLouth singled with one out and took second on a wild pitch. With two outs, Denard Span singled to right, scoring McLouth and ending Leake's night after 110 pitches.
The Reds used their legs to take a 1-0 lead in the fourth.
Frazier was hit by a pitch with one out and went to third on Brayan Pena's single. With Chris Heisey at the plate, Ramos blocked a pitch by Strasburg in the dirt and Pena broke for second. Frazier dashed home when Ramos threw to second and second baseman Espinosa's only play was on Pena, who was tagged out.
Reds C Devin Mesoraco, in his 191st major-league game, hit cleanup for the first time. ... Nationals manager Matt Williams said rookie RHP Blake Treinen will be called up from Triple-A Syracuse to make LHP Gio Gonzalez's scheduled start Thursday in Pittsburgh. Gonzalez (left shoulder inflammation) went on the 15-day DL on Sunday. Treinen has made four appearances, including one start, for Washington. ... Williams said 1B Adam LaRoche (right quad strain) took pregame grounders for the first time since going on the DL on May 10.. Cincinnati's Johnny Cueto (4-2, 1.25) opposes Doug Fister (0-1, 4.76) on Tuesday.