Quarterback Gary Hogeboom threw a pair of 24-yard touchdown passes and the Dallas Cowboys finished the National Football League preseason unbeaten for the first time since 1971 with a 20-10 victory over the Houston Oilers last night in Irving, Tex.

The game-winner came on a 24-yard scoring pass to rookie wide receiver Leon (Speedy) Gonzalez with 4:44 left in the third period. Gonzalez is a seventh-round pick from Bethune-Cookman.

Dallas (4-0) joined two NFC East Division rivals, the New York Giants and the Washington Redskins, as the only unbeaten teams in preseason. Houston finished 1-4.

"You never know how good you are until you tee it up against the best and we'll do that against Washington in the opener," said Cowboys Coach Tom Landry. "Then we'll know where we are for sure."

The Cowboys fell behind, 10-0, in the first quarter, in which they didn't produce a first down.

A 49-yard field goal by Tony Zendejas, acquired last week from Washington, and Warren Moon's 51-yard scoring pass to rookie Mike Akiu, a seventh-round draft pick from Hawaii, put the Oilers ahead. Moon later suffered a ripped nail on his right thumb and sat out the second half.

Dallas came back on a 34-yard field goal by Rafael Septien and a 24-yard touchdown pass from Hogeboom to Tony Dorsett to tie the score at halftime.

Danny White, the Cowboys' starting quarterback, didn't suit up as a precautionary measure because of a rib injury.

Dallas is 15-4 against the Oilers in the annual battle for Texas bragging rights and has beaten the Oilers seven straight times in the preseason.