The Cardinals lost three of four at Nationals Park and five of six overall while trying to hold off Pittsburgh for the final NL wild-card berth.
St. Louis remains one game ahead of Pittsburgh in the race for the final playoff spot. After a grueling road trip, there are worse places to be.
"Our goal is to make it to the playoffs and we're right where we want to be as far as that's concerned," outfielder John Jay said. "I still like the shape our team's in. I think we're going to be all right."
St. Louis began its trip by scoring 22 runs in winning three of four from NL Central rivals Cincinnati and Pittsburgh. During the final six games, the Cardinals were outscored 45-13 to finish at 4-6.
Strasburg had something to do with the Cardinals early troubles in the finale.
"Strasburg threw the ball well, kept us at bay," St. Louis manager Mike Matheny said. "Walking out of here after a tough trip 5-5 would've been real nice."
The NL East-leading Nationals took three of four from St. Louis and passed their 80-win total from last season.
Strasburg, rocked for seven runs last Tuesday at Miami, left with a 2-0 lead and a 2.94 ERA. He threw 97 pitches and wound up with a no-decision.
The 23-year-old Strasburg has struck out a league-leading 195 in 156 1-3 innings this season. The Nationals have repeatedly stated they intend on shutting him down in his first full season since undergoing Tommy John surgery in 2010.
The Nationals have been vague about an innings limit, but the team sat Jordan Zimmermann at 161 1-3 innings last season in a similar situation.
Nationals manager Davey Johnson said on Thursday that Strasburg is probably down to "two or three" starts, meaning the final one could come Sept. 7 at home against Miami or Sept. 12 at the New York Mets.
Ian Desmond and Danny Espinosa produced two-out RBI singles in the seventh that lifted Washington. Kurt Suzuki homered and drove in two runs for the Nationals.
The Cardinals rallied in the seventh after Strasburg left with three hits against reliever Sean Burnett, including Daniel Descalso's two-run homer.
Washington responded with four consecutive two-out singles against Lance Lynn (13-6). Desmond's flare to center scored pinch-runner Eury Perez with the go-ahead run. Espinosa had three of the Nationals' 13 hits.
Ryan Mattheus (2-3) pitched 1 1-3 innings, allowing a run on Tony Cruz's RBI double in the eighth. Tyler Clippard, the worked the ninth for his 29th save.
Lynn pitched one inning, allowing two runs on four hits for the Cardinals, who have lost five of six while trying to hold off Pittsburgh for the final NL wild-card berth.
Facing the Cardinals for the first time, Strasburg gave up Matt Holliday's two-out double in the first. The All-Star ace held St. Louis without another hit until Holliday's sixth-inning single.
Strasburg walked one overall. He fanned at least two hitters in four innings and regained the NL strikeout lead by whiffing St. Louis pitcher Jake Westbrook in the fifth.
Third baseman Ryan Zimmerman's throwing error, a walk and a wild pitch put runners on the corners with one out in the fourth. Holliday attempted to score the game's first run on Bryan Anderson's shallow fly ball to right, but Bryce Harper easily threw him out at the plate for the final out.
Usually in center, Harper shifted to right with Jayson Werth scratched from the lineup minutes before the first pitch.
Suzuki, acquired in a trade with Oakland last month, stroked his third homer on the season in the bottom half. In the sixth, he tacked on a third consecutive single against Westbrook, which scored Desmond and ended Westbrook's day.
Westbrook allowed two runs on nine hits with six strikeouts and one walk. He avoided his third loss in four starts when Descalso turned on a 3-1 pitch from Burnett for his fourth home run of the season.
"It was a lot better today than the last two starts," said Westbrook, strafed by Houston and Pittsburgh for 12 runs and 18 hits in 10 innings. "It was kind of a grind all day, but I was able to make some decent pitches."
NOTES: Matheny rested All-Star catcher Yadier Molina and infielder Skip Schumaker. ... St. Louis returns home Monday and has Joe Kelly facing Mets starter Collin McHugh.