ARLINGTON, Texas -- As they have so often -- and in a finish befitting their historic rivalry -- the San Francisco 49ers and Dallas Cowboys battled to the bitter end of Sunday's nostalgic NFC wild-card meeting.

Ultimately, a strong Niners defensive effort combined with myriad Dallas mistakes allowed San Francisco to emerge with a 23-17 victory in the first postseason meeting between the teams since 1995, and the first matchup between two franchises with at least five Super Bowl victories apiece.

In the process, the 49ers became the first underdogs (+3.5) and road team to win in this postseason. It's a victory that comes 40 years and a week after "The Catch" in the 1981 NFC Championship Game, and one that will hold special meaning for 49ers coach Kyle Shanahan, whose father, Mike, was the Niners' offensive coordinator for some of the famous meetings between these teams in the 1990s.

The Niners' win moves them to 3-5 all time against Dallas in the playoffs and sets up an NFC divisional matchup against another historical rival, the Green Bay Packers, next weekend.

None of it would have been possible without a big assist from the Cowboys. Dallas, the No. 3 seed in the NFC, repeatedly made key mistakes throughout the game, including a Dak Prescott interception that turned into a 49ers touchdown.

The Cowboys racked up 14 penalties -- tied for the most in a playoff game in franchise history -- for 84 yards. Many of those came in key moments, including third downs, to keep San Francisco drives alive.

The Niners made some of their own miscues in the fourth quarter, including an interception from quarterback Jimmy Garoppolo to set up a Dallas touchdown.

"Yeah the interception just ... got away from me," Garoppolo said. "Those are the easy layup ones you just got to make."

As only a San Francisco-Dallas playoff game could provide, all of that led to significant drama in the closing moments. The Niners' 23-7 lead evaporated as Dallas trimmed it to 23-17. The 49ers gave the ball back to the Cowboys with a late punt after a delay of game penalty moved the Niners from fourth-and-1 to fourth-and-6.

The Cowboys quickly got in San Francisco territory with a 38-yard pass to tight end Dalton Schultz. But the 49ers' defense, as it had all game, delivered when it needed to most, even without linebacker Fred Warner (ankle) and defensive end Nick Bosa (concussion), both of whom departed during the game and did not return. The 49ers' defense played just 23 snaps all regular season with Bosa and Warner both off the field.

"Still trying to figure out where I'm at -- it was pretty emotional out there," Shanahan said. "Lots of opportunities I thought we had to win the game -- I felt like we did on a number of times -- but those guys just kept fighting.

"And we had a couple mistakes there at the end that shouldn't have let it get there; just for the guys to come out and finish that game, especially in that environment, it was a hell of a win by the guys."

Garoppolo described it as "an emotional game" of highs and lows, but said it never felt like the game was getting away from the 49ers.

"I always felt like we were in control of the game, but just made for some good TV I guess," Garoppolo said with a laugh.

Garoppolo finished 16-of-25 for 172 yards with no touchdowns and the interception for a passer rating of 67.4. Prescott was 23-of-42 for 254 yards with a touchdown and an interception for a passer rating of 65.7.

The Niners and Cowboys entered Sunday's meeting with a combined 67 playoff wins, tied for the most ever entering a playoff matchup. Dallas had won its past three wild-card games, all at home, before Sunday's defeat. The 49ers improved to 4-1 in road playoff games since 2012 after going 2-9 in franchise history prior to that.

Traditionally, the winner of a 49ers-Cowboys playoff game has gone on to postseason success. The winner of five of the previous seven postseason meetings, including each of the past four, has gone on to win the Super Bowl.