SAN FRANCISCO (AP) — In one triumphant afternoon, playoff first-timer Alex Smith joined a pair of 49ers Hall of Fame quarterbacks with his own indelible postseason moment.

Joe Montana had “The Catch.” Steve Young had “The Catch II.” Now, Smith added another epic play to the 49ers’ storied history: “The Grab.”

Smith completed a 14-yard touchdown pass to Vernon Davis with 9 seconds left just after Drew Brees had put the high-powered Saints ahead, and resurgent San Francisco capitalized on five New Orleans turnovers for a thrilling 36-32 playoff victory Saturday.

“You’ve got to call it ‘The Grab,’” Davis said of his play. “We were down. I had to make it happen to take my teammates where we want to go.”

What a way to celebrate the 30-year anniversary of “The Catch.”

Montana to Dwight Clark then. Smith to Davis now.

Smith ran for a 28-yard TD with 2:11 left and threw another scoring pass to Davis in the first quarter. Coach Jim Harbaugh’s NFC West champions (14-3) proved that a hard-hitting, stingy defense can still win in the modern, wide-open NFL by holding off one of league’s most dynamic offenses.

“This is huge for us,” Davis said. “It’s history, legendary, anything you can describe.”

Brees completed a 66-yard touchdown pass to Jimmy Graham with 1:37 left and the Saints seemed poised to rally from an early 17-point deficit when Smith and Davis delivered once more. It was a wild back-and-forth finish featuring an impressive passing duel over the waning moments.

Their highlight show came in the opposite end zone from where Clark caught a stretched-out 6-yard pass from Montana on Jan. 10, 1982. Saturday’s game-winner by a leaping Davis — who plowed over a defender as he landed — came in the same end zone where Steve Young hit Terrell Owens for a winning TD with 3 seconds left in a 30-27 wild-card win over the Packers in the 1999 playoffs. T.O.’s grab became known as “The Catch II.”

San Francisco triumphed in its first playoff game in nine years and will move on to face the New York Giants or defending champion Green Bay Packers, who play Sunday. A win by the Giants would give the 49ers the home field.

The 49ers pulled off another last-second win in a season full of them — and on a day former coach George Seifert served as honorary captain for the coin toss. San Francisco came from behind for five victories during the regular season, four on the road.

Smith helped the Niners become the first team in NFL history to score two lead-changing touchdowns in the final 3 minutes to win a playoff game, according to STATS LLC.

Davis, who wept on the sideline afterward days after saying he was overwhelmed early on by Harbaugh’s thick playbook, finished with seven catches for 180 yards. It was the most yards receiving by a tight end in a playoff game. He averaged 25.7 yards per catch.

Smith found Davis for a 47-yard completion on a cross to the left sideline with 31 seconds left and Smith then connected with Frank Gore to put the Niners on the 14 for third down. Davis produced on a play they call “Vernon Post” — one they worked on all week, just from the right side instead of the left where it worked Saturday.

Brees came up big down the stretch just as he did throughout a record-setting season, also hitting Darren Sproles for a 44-yard TD with 4:02 remaining — one of Sproles’ 15 catches for 119 yards.

“It stings right now because of the expectation level that we had coming into this tournament and understanding that if we win here we’re into the NFC championship game and anything can happen,” Brees said. “That’s tough. Tough to swallow at this point.”