The Nationals' 6-5 win also eliminated Bryce Harper's Phillies from postseason eligibility. Turner was 2 for 4 with four RBIs and a run scored. Harper -- who left the Nationals to join the Phillies this off-season -- hit a pinch-hit homer in the loss.
"It was just a big hit and a big game all around. It was a big team win," Turner told MASN.
The Nationals (88-69) earned their first Wild Card berth in franchise history after the Pittsburgh Pirates handed the Chicago Cubs their seventh consecutive loss. Washington also won the first game of Tuesday's doubleheader 4-1 before earning their second victory of the day.
Nationals ace Max Scherzer allowed five hits and four runs while tossing 10 strikeouts in six innings to pick up his 11th win of the season. Aaron Nola took the loss for the Phillies after allowing five hits and five runs in 5.2 innings.
Washington lost Harper in free agency and was at one point this season 12 games under .500, before rallying back into the playoff picture.
"We're going to have plenty of time to reflect on the fact we didn't get to the postseason, which was the goal and the only thing that we thought about all season long," Phillies manager Gabe Kapler told reporters. "We'll get there. We'll get to that moment of reflection. It felt some sting already, I think we're going to continue to feel some sting."
Brad Miller put the Phillies ahead with a three-run homer in the top of the first inning. Nationals catcher Yan Gomes responded with a solo homer in the third frame. Miller came back to the plate in the fourth frame and smacked a solo shot off Scherzer for a 4-1 lead.
Gomes cut the Phillies' lead in half with an RBI sacrifice fly in the bottom of the fourth inning. Asdrubal Cabrera took a walk from Nola to leadoff the bottom of the sixth frame. Nola struck out Matt Adams before allowing a single to Victor Robles. He fanned Gomes with another strikeout before walking Howie Kendrick to load the bases.
Jared Hughes entered the game in relief of Nova and began a short exchange with Turner. Hughes got a called strike before tossing in a sinker. Turner throttled the offering over the left center field fence for a go-ahead grand slam, giving Washington a 6-4 edge. The 378-foot blast left the field in 5.4 seconds, according to Statcast.
Harper hit his 34th homer of the season in the third at-bat of the seventh inning, but the Nationals' bullpen silenced the Phillies' bats down the stretch. Daniel Hudson earned his seventh save of the season after pitching a hitless ninth inning.
"In spring training I said I don't know if it's going to be this year or next year or the next," Harper said. "It takes time to build something special. As a team and an organization, (the Phillies) have been there. They were there in '08 and '09 and they built it up to be the team that they were with trades and things like that. I think this franchise is going to do that."
Harper also backed Gabe Kapler as the Phillies' future manager.
The Phillies (79-78) battle the Nationals again at 7:05 p.m. EDT Wednesday in Washington, D.C.