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

Soon afterward, the two dapped each other up and embraced; McVay then tapped him on the helmet as the team jogged to the sideline ahead of 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 on vacation in Cabo San Lucas, Mexico. They joined forces hoping to play in meaningful games this January and later.

Monday marked 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 touchdowns 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 and soon led 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.

“I’m very pleased with him and looking forward to playing clean ball in the postseason, trusting his teammates, playing the way that he’s capable of,” McVay said. “If he just plays within himself, I trust really good things will happen for this team.”

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.

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 ahead of 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 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 doomed his team against quality competition.

That was not the case on Monday night.

In the first quarter, instead of force-feeding Cooper Kupp, who was double teamed in the end zone, Stafford smartly found Odell Beckham, Jr. in single coverage, who then made an acrobatic leaping catch for a 4-yard score.

He placed passes accurately for his receivers, who created separation and yards after the catch all night from the Cardinals’ defensive backs. Beckham Jr., who also faces his own postseason reckoning, caught the first playoff touchdown of his eight-year career, and, for style points, laced a 40-yard pass to Cam Akers on a third-quarter touchdown drive.

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