Roger Staubach threw three touchdown passes and the Dallas defense made it 11 straight quarters without allowing a touchdown yesterday in a 24-3 victory over the New York Giants in Texas Stadium.

The Cowboys remained two full games behind the unbeaten Redskins in the National Football Conference East race with a 4-2 record. The Giants are tied with Philadelphia at 3-3 for third place.

Staubach completed 17 of 32 passes for 246 yards before being replaced by Danny White with about three minutes remaining.

Staubach was sacked five times and was intercepted once, in the fourth quarter in the New York end zone.

The Cowboys sacked two New York quarterbacks eight times and sent Giant fullback Willie Spencer to the bench early with a hip pointer.

Dallas running back Tony Dorsett was held to 73 yards on 17 carries by the New York defense.

The Redskin victory over Detroit was announced over the public address system here two minutes after the opening kickoff and there were mostly boos, but possibly a few others from the U.S. Marine Corps drum and bugle corps from Washington, D.C., which performed at halftime after the Cowboys built a 14-3 lead.

The Cowboys went 70 yards to score in the first quarter on runs by Tony Dorsett and passes by Roger Staubach to Dorsett for 15 yards and 17 yards to wide receiver Tony Hill, for a touchdown.

Joe Pisarcik took the Giants 52 yards before Joe Danelo kicked a 37-yard field goal on the first play of the second period. A 44-yard pass from Pisarcik to wide receiver Jimmy Robinson ate up most of the distance.

The Cowboys got rolling again near the end of the half and went 69 yards to score, the final 23 yards on a pass from Staubach to tight end Billy Joe DuPree. A roughing-the-passer penalty against Giant limebacker Brian Kelley and 17- and four-yard runs by Staubach put Dallas in scoring position.

Pisarcik suffered a jaw injury shortly after that and was replaced by Terry Golsteyn.

The Cowboys ran their advantage to 21-3 in the third quarter on Staubach's third touchdown pass, 30 yards to Hill.

Again a roughint-the-passer penalty against the Giants started a Dallas drive that went 67 yards. Hill got far behind right cornerback Ray Rhodes, who might have been distracted by DuPree also running in the general area.

In the fourth quarter, Dalls drove 63 yards to the New York four before Rafuel Septien kicked a 22-yard field goal.

Wide receiver Hill caught 26 and 10-yard passes and Dorsett ran four yards to the four. On a third-down play, former St. Louis Cardinal tight end Jackie Smith was inserted and Staubach led him a bit too far on a pass in the flat. Septien then kicked his three-pointer for the final Dallas points.