Olsen (1-3) allowed one run and six hits, striking out six. Garrett Mock pitched 1 1-3 hitless innings, Kip Wells worked the eighth and Julian Tavarez finished for his first save since May 28, 2006, for Boston.
"One thing about him is he'll throw strikes," Nats manager Manny Acta said of the well-traveled Tavarez. "That's one thing we know he'll do. They'll either hit him or he'll get them out. He takes the walks out of the equation."
Olsen shut down an offense that scored 33 runs in the previous three games, including 20 against Nationals pitching.
The Nationals, who have the worst record in the majors at 5-15, avoided being swept for the fourth time this month. They got a rare flawless performance from a relief corps that has blown six saves and is a combined 0-7.
Joel Hanrahan had been Washington's closer until he allowed Raul Ibanez's game-winning grand slam in a 13-11 loss on Monday night. It was his third blown save in five chances.
"We know we are better than our record shows in this clubhouse," Olsen said.
Anderson Hernandez had three hits and drove in two runs for Washington out of the No. 8 spot in the lineup.
"He's gotten a lot better lately," Acta said. "He's getting quality at-bats and is very confident. That's why we like him back in the lineup."
Shane Victorino hit a solo homer for the Phillies. Brett Myers (1-2) gave up three runs and eight hits in six innings.
"I thought I did a good job of locating my pitches, but other than that, not much I can take from it other than I got beat," Myers said.
Elijah Dukes and Hernandez hit RBI singles in the sixth to put the Nats ahead 3-1. Ryan Zimmerman led off the inning with a double to left-center, extending his hitting streak to 18 games.
After Adam Dunn struck out, Dukes hit a grounder up the middle to score Zimmerman. Hernandez hit a two-out single to right-center to drive in Dukes.
Olsen left after allowing singles to Ryan Howard and Ibanez in the sixth. Mock came in and retired Pedro Feliz on a fly ball to end the threat.
Victorino hit a liner to the seats in left to give the Phillies a 1-0 lead in the first. Olsen struck out four in a row after the homer and six of the next eight batters.
The Nationals tied it at 1 in the third when Myers had control problems. After Hernandez hit a one-out double, Myers walked Olsen. He walked Nick Johnson to load the bases with two outs and walked Zimmerman to force in a run.
"You have to get the eight-hole hitter and pitcher out in the National League," Phillies manager Charlie Manuel said.
Olsen pitched out of a bases-loaded jam in the fourth, retiring Chris Coste on a grounder to third to end the inning. Zimmerman made a fine play going to his right, and his strong throw to first beat the slow-footed Coste.
"They made adjustments the second time around the lineup," Olsen said. "I made counter adjustments and we were able to escape the fourth without any damage."
Olsen has pitched well in his last three outings after two poor starts. The left-hander has lowered his ERA from 14.63 to 6.08 in that span.
Notes: Phillies ace Cole Hamels and closer Brad Lidge each will throw bullpen sessions Friday. Hamels left his start Tuesday night after injuring his left ankle in the fifth inning. Lidge hasn't pitched since Sunday because of inflammation in his right knee. ... Nationals SS Cristian Guzman returned to the lineup after missing 12 games with a strained left hamstring. ... Victorino has a 10-game hitting streak. ... Zimmerman's hitting streak is the longest in the five-year history of the Nationals, who were the Montreal Expos.
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