Gary Hogeboom, the eagerest young aspirant to Dallas quarterbackdom since Roger Staubach, stumbled and then soared to storybook victory tonight over the Los Angeles Rams.

The lean, boyish 26-year-old, best remembered for almost aborting the Washington Redskins' trip to a Super Bowl victory, completed a team-record 33 of 47 passes for 343 yards to beat the ice-cold Rams, 20-13.

Despite an early fumble that gave Los Angeles an easy touchdown, Hogeboom moved the Cowboys confidently through several mishaps, including four turnovers in the first 16 1/2 minutes, before they finally pulled away in the last few minutes for their 19th victory in 20 season openers and the 235th victory of Tom Landry's NFL coaching career, second to George Halas' 325 NFL victories.

Landry, who had trouble pronouncing Hogeboom's name when he announced the switch last week, said his new quarterback "was outstanding. He started tough and the most impressive thing was he hung in and won the game."

Tonight's game brought a holiday crowd of 65,403 into Anaheim Stadium, the second highest attendance ever for a Rams game here.

The Rams took a 13-7 halftime lead, but Hogeboom was pushing the home team around in his first NFL start.

Hogeboom, a short but vivid nightmare from the Washington Redskins' past, fumbled to set up the Rams' initial touchdown and threw an interception in the first quarter. But by the end of the half, he had completed 21 of 25 passes for 240 yards, including a 19-yard touchdown to tight end Doug Cosbie.

Dressed in T-shirt and game pants, sipping a tiny can of cola, Hogeboom conducted a postgame press conference with the guileless joy of a newcomer to the art. "I'm just glad it's over," he said. "This last week was tough, but when the game started, I was real relaxed. I had fun."

Far more popular with his Dallas teammates than the remote nine-year veteran Danny White, Hogeboom was picked to start a week ago after a good preseason.

White said he was glad the new starting combination "proved sound, that's what's important." But he added that watching from the sidelines "was a lot less fun than I hoped it would be . . . It's not my intention to do this the rest of my career."

Before this start, Hogeboom had little experience, except for the frantic second half of the January 1983 NFC championship game against the Redskins. With White benched by a concussion, Hogeboom revived a faltering offense with two touchdown passes, only to see two interceptions pull the game out of his reach.

On the first play of his second series tonight, Hogeboom was looking for a receiver to his right when linebacker George Andrews jumped him. The ball popped out and into the hands of defensive end Jack Youngblood, who carried it to the two-yard line.

Last year's rookie of the year, Rams running back Eric Dickerson, who finished with 138 yards on 21 carries, scored the touchdown.

Hogeboom, with substantial help from running back Tony Dorsett, moved the ball to the Rams' 42 on the next series, then underthrew a pass intended for wide receiver Doug Donley. Cornerback Gary Green intercepted and returned the ball 23 yards, setting up Mike Lansford's 31-yard barefoot field goal. Lansford followed with a 36-yard field goal for a 13-0 lead.

Not noticeably upset, Hogeboom began to reach his receivers almost at will. A good drive set up by a 43-yard pass to Donley (nine receptions) ended prematurely when Dorsett fumbled on the Rams' five-yard line -- one of three fumbles Dorsett turned over to the Rams. Cowboys strong safety Dextor Clinkscale intercepted a Vince Ferragamo pass at the Cowboys' 17, and this time, Hogeboom took full advantage of his chance.

A 17-yard pass to Donley and a 19-yard pass to Tony Hill took Dallas to the Rams' 19. Hogeboom then arched one more into the outstretched arms of Cosbie on the left sideline at the two-yard line and he stumbled in to score.

In the third quarter, with the Rams' offense sputtering, Hogeboom took Dallas to the 14-yard line before giving way to Rafael Septien, who kicked a 31-yard field goal.

Ferragamo responded with another luckless series of downs, ending in a 40-yard pass that just missed Henry Ellard's outstretched fingers.

Moving with confidence, emboldened by a series of Dorsett runs that put him ahead of Joe Perry's seventh-leading NFL yardage record of 8,388, Hogeboom moved back toward the Rams' goal line. He hit Cosbie for 13 yards on a third-and-11 play. An interference call against cornerback LeRoy Irvin moved the Cowboys across midfield.

A fumble by Dorsett gave the ball to the Rams, but Ferragamo soon gave it back with his third interception, picked off by linebacker Mike Hegman. For once, Hogeboom could not move the ball, but Septien kicked a 52-yard field goal, one yard short of his personal record, for a 13-13 tie as the fourth quarter began.

Dickerson effortlessly loped through the Dallas line, but the Rams' passing attack could not click even 55 minutes into the game. In desperation, the Rams had Dickerson try a long pass to Mike Guman; it fell like a beach ball into cornerback Everson Walls' waiting hands.

Dallas moved to seal the Rams' fate in the last five minutes. Hogeboom fired a 12-yard pass to Donley at the Rams' seven. Dorsett then plunged ahead for the touchdown with just under four minutes left, putting the Cowboys ahead, 20-13.