SEATTLE — In a game they very much needed to win, and against an opponent that gave them everything they could handle, the Seattle Seahawks are still alive in this season’s NFL playoff chase because they persevered Sunday afternoon in a back-and-forth showdown with the Pittsburgh Steelers.

Three times Seattle took the lead and three times Pittsburgh took the lead right back. But in the final period the Seahawks were able to move in front a fourth time, and this time they held on for a dramatic 39-30 victory at noisy CenturyLink Field.

The outcome — one that head coach Pete Carroll called “a really strong win” — moves Seattle above .500 for the first time this season at 6-5 with five games remaining. The Seahawks, bidding for a third straight Super Bowl appearance, are squarely in the running for a wild-card berth with a division title also possible, although the latter scenario is increasingly unlikely after NFC West rival Arizona improved to 9-2 with a 19-13 win over San Francisco on Sunday.

Seattle’s margin for error to make the playoffs remains “small,” acknowledged defensive end Cliff Avril, and “it all boils down to us winning. … There’s still a lot of football games to be played, and if we continue to keep building I think we’ll like our record at the end of the season.”

Added quarterback Russell Wilson, who overcame an apparent overnight bout with the flu to throw a career-high five touchdown passes: “(This was) a huge win against a very, very good football team. … We hung in there, kept battling, played relentless football and we found a way to win.”

The victory was costly, too. Seattle tight end Jimmy Graham injured his right knee early in the fourth quarter and will miss the rest of the season with a knee injury.

That was the worst news for the Seahawks in a game of contrasts. Seattle gave up a franchise-record 456 passing yards to Steelers quarterback Ben Roethlisberger, but also got four interceptions (two off Roethlisberger, two off backup Landry Jones). And when the Seahawks surrendered a fourth-quarter lead — something that has happened in their five defeats this season — they countered with two late touchdown passes to wide receiver Doug Baldwin, the second covering 80 yards in the closing minutes.

Pittsburgh’s last-gasp possession ended when Seattle safety Kam Chancellor made a leaping interception of a tipped pass with 1:45 to play in the game. The Seahawks managed one first down and were able to run out the final seconds.

“There were a lot of exciting things that happened in this football game,” said Carroll, who added, “(The Steelers) challenged us to the max, (but) we had what needed today to get it done.”

“It’s about finishing,” said Seahawks wide receiver Jermaine Kearse. “There’s a couple of games we didn’t finish (this season), and Pete’s always going to preach about how it’s not how you start, it’s about finishing the game. … It comes down to who’s going to make the plays (at the end), and I felt like we did that today.”

Said Baldwin: “This is an unbelievable win for us. Don’t discredit the Steelers — they came in with a wonderful game plan and they fought really hard — but fortunately we were able to pull it out.”

Ahead for the Seahawks are road games against Minnesota and Baltimore the next two weeks. The schedule then brings the Seahawks back to Seattle for games against Cleveland and St. Louis before the regular-season finale at Arizona.

The Seahawks will make the playoffs if they win their remaining games, and almost certainly will advance by winning four of five. But two losses would mean a 9-7 record, and that might leave them out of the postseason for the first time since 2011.

“We have to get on top of this .500 thing and get going here if we’re going to have a chance,” Carroll said. “As we continue to play football, if we can count on winning games in tough situations in a number of different ways … it gives us the chance and the hope that we can go get another one.

“And that’s all that it is right now,” he said. “It’s a one-game opportunity going forward and now we’ll see if we can get another one.”