SAN FRANCISCO (AP) — What a way to celebrate the 30-year anniversary of “The Catch.”

Joe Montana to Dwight Clark then.

Alex Smith to Vernon Davis now.

Smith completed a 14-yard touchdown pass to 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.

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

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.

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.”

How about this one?

“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.”

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.

Davis, who wept on the sideline afterward days after saying he was overwhelmed early 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.

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.”

The 49ers also showed that defense can still dominate in the days of big passers like Brees.

With Donte Whitner bringing the bruising hits and Dashon Goldson, Patrick Willis and their defensive mates pressuring Brees and forcing turnovers from every angle, surprising San Francisco is a win away from returning to the Super Bowl for the first time since capturing the proud franchise’s fifth championship after the 1994 season.

Brees, whose team was coming off consecutive 600-yard games, completed 40 of 63 passes for 462 yards and four touchdowns and was sacked three times. He also threw two interceptions, his first in the postseason in five years, and New Orleans (14-4) fell short again in its quest to get back to the Super Bowl after winning it all two years ago. The Saints are still searching for the first postseason road victory in franchise history after falling to 0-5.

“Kind of an unbelievable game the way it went back and forth,” New Orleans coach Sean Payton said. “It’s obviously a difficult game to lose.”

How far these 49ers have come since that 24-3 trouncing they took back in August at the Superdome in the teams’ exhibition opener. Now, Harbaugh’s “Who’s got it better than us? No-body!” group is drawing comparisons to the good ol’ days of Montana, Jerry Rice, Ronnie Lott and Steve Young. And of course, Dwight Clark, who came through with “The Catch” to beat Dallas in the NFC title game on Jan. 10, 1982.

All-Pro David Akers, the Niners’ most experienced playoff veteran whose 44 field goals set a single-season record, kicked three more when it mattered most — from 25, 41 and 37 yards.

The underdog 49ers made the big plays on both sides of the ball and on special teams.

“Guys were so confident, as long as we had time we had a shot,” Smith said.

They also had a towel-waving sellout crowd of 69,732 behind them at Candlestick Park on a beautiful sunny winter day in the Bay Area. It was 62 degrees at kickoff.

Who Dat? It’s the Saints headed home to the Big Easy empty-handed.

A year ago, New Orleans came out West and suffered a stunning loss to the 7-9 Seattle Seahawks in the NFC wild-card round.

The Saints had lost five fumbles all season, then gave three away Saturday against San Francisco’s opportunistic defense that pressured all day.

Harbaugh’s theme “don’t overcook it,” rang true as the 49ers relied on what got them here — perhaps the league’s best defense and special teams.

Brees drove the Saints close to the goal line on their opening drive but Pierre Thomas lost that fumble and was lost for the game to a head injury after being hit by Whitner. Two other turnovers came on special teams.

Smith, the 2005 No. 1 overall draft pick booed so often his first six seasons, hit Davis on a 49-yard touchdown pass in the first quarter and then Michael Crabtree on a 4-yard TD strike as the 49ers jumped out to a quick 17-0 lead. He finished 24 for 42 for 299 yards with a 103.2 passer rating.

“It shows he’s becoming an elite quarterback. I’m glad the world could see what he did today,” Willis said.

Smith and his offense were determined to make their mark on these playoffs after being overlooked all season, and showed a little flair of their own. Davis dunked the football over the goal post after his score to make the Niners’ most significant game on the NFL’s big stage since rallying to stun the New York Giants in January 2003.

Brees threw two first-half interceptions and had his NFL-record streak of 226 postseason passes without an interception snapped on Goldson’s pick in the opening quarter. Brees’ streak dated to the NFC championship game against Chicago five years ago.

But he hit a well-guarded Graham for a leaping 14-yard touchdown catch at the 9:32 mark of the second quarter, then had a 25-yard TD completion to Marques Colston to send the Saints into halftime trailing only 17-14.

Any momentum New Orleans gained was hurt when Colin Jones forced return man Sproles to fumble after the 49ers punted on their first possession of the second half. That set up Akers’ second field goal of the day.