INGLEWOOD, Calif. — Thirty minutes before the biggest game of Matthew Stafford’s N.F.L. career, he tossed passes in warm-ups with his coach, Sean McVay, standing close by.

Soon afterward, the two dapped each other up and embraced; McVay then tapped Stafford on the helmet as the team jogged to the sideline before the formal player introductions.

It has been nearly a year since the partnership was formed between McVay and Stafford, then the frustrated face of the moribund Detroit Lions, when both of them were eliminated from the postseason and coincidentally on vacation in Cabo San Lucas, Mexico, at the same time. They joined forces hoping to play in meaningful games this January and later.

Monday was a crucial step toward that vision, when the Rams defeated the Arizona Cardinals, 34-11, in the N.F.C.’s wild-card round, the first playoff win of Stafford’s 13-year career.

Stafford completed 13 of 17 passes for 202 yards and a touchdown with no interceptions and advanced the Rams to this weekend’s divisional round, where the team will play at the No. 2-seeded Tampa Bay Buccaneers on Sunday.

The Rams defense intercepted Kyler Murray twice on back-to-back drives in the second quarter, returning one for a touchdown that put Los Angeles ahead, 21-0. Running backs Sony Michel and Cam Akers rushed for a combined 113 yards, and McVay smartly challenged two officiating calls that were reversed, soon leading to points.

Stafford’s play may not have won the Rams the game, but neither did the late-game interceptions that have been his calling card doom them. It’s a performance he said he was happy with, and he later downplayed the significance of his first January win, saying, “that’s more important for you guys.”

“I just want to be a part of this team and help us win,” Stafford continued. “I’m trusting myself, trusting my abilities, trusting my teammates. We’ll go out there and play and let the chips fall where they may.”

Shortly before checking into the resort last year, an agitated McVay sat in a videoconference with reporters after his team’s loss to the Packers in the divisional round and complimented the poise and performance of Aaron Rodgers. He did not offer kind words for his quarterback at the time, Jared Goff, and did not say definitively that Goff would return for the 2021 season.

He wanted an upgrade. Though Goff led Los Angeles to a Super Bowl in 2018, he regressed, throwing 29 interceptions in the next two seasons.

Enter Stafford, who had lost the only three postseason games he played in with the Detroit Lions despite throwing for 45,109 career yards, fifth among active passers entering this season.

McVay convinced General Manager Les Snead to trade for Stafford in a blockbuster exchange that included Goff and two future first-round draft picks, the team going all in on building a championship-caliber roster before this season’s Super Bowl, which the Rams will host.

The early returns on Stafford’s trade and the star acquisitions that followed — linebacker Von Miller and receiver Odell Beckham Jr. joined in midseason — have been positive. The Rams won 12 games and claimed the N.F.C. West, and Stafford threw for 4,886 yards and 41 touchdowns. But his 17 interceptions were tied for the league lead and often derailed his team against quality competition.

That was not the case on Monday night.

Stafford placed passes accurately for his receivers, who created separation and yards after the catch all night from the Cardinals’ defensive backs. In the first quarter, instead of force-feeding Cooper Kupp, who was double teamed in the end zone, Stafford smartly found Beckham in single coverage. He made an acrobatic leaping catch for a 4-yard score.

With such a definitive victory under his and the Rams’ belts, Stafford may well see more career-defining games in the weeks to come.

“I’m just so lucky to be able to do this with him,” McVay said after the game. “He’s our leader. We wouldn’t be here without him. For him to play under such control in that game plan — yeah, I think it was a combination of everything.”

Beckham, who also faces his own postseason reckoning after his high-profile exit from the Cleveland Browns, caught the first playoff touchdown of his eight-year career, and, for style points, laced a 40-yard pass to Akers on a third-quarter touchdown drive. But Akers was disappointed in the ball’s precision as it hung in the air.

“He probably should have led me a little bit,” Akers said with a chuckle.

There were no jokes for the Cardinals, as Monday’s result concluded a disappointing season anticlimactically. Arizona burst to an 10-2 record, but lost six of their last seven games. The star receiver DeAndre Hopkins did not play with a knee injury he sustained in Week 14, despite the team’s hopes that he could return for the playoffs. Once considered the best offense in the league, the Cardinals generated only 198 yards, and the Rams defense hit Murray five times.

Tight end Zach Ertz and receiver A.J. Green, who were added this season, combined for only 21 yards, and the veteran defensive end J.J. Watt returned after not playing since Week 7 with a shoulder injury, posting three tackles. Both Murray and Coach Kliff Kingsbury had not been to the playoffs in their young N.F.L. careers. Neither were proud of the result. It pushed Kingsbury’s record to 24-25-1 in his three seasons as coach, and Murray completed only 55.9 percent of his passes for 137 yards.

“It’s disappointing that we didn’t make it a game and come out and play the football we know we’re capable of playing,” Murray said. “Losing is one thing, but when you don’t even make it competitive, it’s another thing.”