Alex Falcinelli's 37-yard field goal with 3:02 remaining brought fumbling, stumbling Rutgers a 3-0 victory over Virginia tonight.

Rutgers, hamstrung by six turnovers, drove 60 yards in 14 plays to set up the score. The decisive drive, which had three third-down conversions, came after Virginia's Wayne Morrison had sent a 30-yard attempt wide with 10:15 left.

There was a noticeable difference in the teams' approaches to the field-goal situations. Rutgers ran the ball toward the middle of the field to make Falcinelli's task as easy as possible. Virginia, throwing on third and nine, came up one yard short with a sideline pass and Morrison was forced to take his soccer-style swing from a sharp angle to the right.

"At that point we hoped we could move the ball in," said Virginia Coach Dick Bestwick. "We asked Wayne if he had any problem kicking from there and he said no. Obviously, we didn't expect any trouble from that close, either. We did consider going for the first down, but we'd missed on three short third-down situations earlier."

In the second period, Morrison was closer with a 50-yard attempt that sailed inches wide of the right post.

After Falcinelli's winning kick, backup quarterback Gordie Whitehead hit three straight passes to move the Cavaliers from their 26 to the Rutgers 32. Going to the air a fourth time, Whitehead was intercepted by Mark Pineiro at the goal line as he failed to reach Henry Johnson in the end zone.

"The free safety cheated over, so they had double coverage," Whitehead said. "I should have hit Henry anyway, but I just underthrew it. We got rolling at the end, but just that one play . . . I was positive we'd score."

This was the second straight year a field goal by Falcinelli and a miss by Morrison decided the game. Rutgers won, 19-17, on a 41-yard kick in the last minute in 1980.

"When your defense turns the ball over as many times as ours did and you don't put any points on the board, you have to look and see what you're doing and find the people to do it," Bestwick said. "Tonight our offensive line was young and not very offensive."

Virginia, playing without injured tailback Quentin Walker, was limited to 31 yards rushing in 32 carries. It had only two first downs in the first half and, when asked what he said to his team at halftime, Bestwick said, "You don't really want to hear that."

Rutgers' offense was seriously affected by the first-period departure of fullback Bryant Moore with a shoulder separation. His replacement, Ted Bethune, fumbled the ball away at the Virginia 10 shortly after Moore left. It turned out to be the only serious scoring threat for either team.

Rutgers tailback Albert Ray gained 111 yards in 34 carries, but his longest was only a nine-yarder. The defenses dominated on both sides: there were eight interceptions, four by each team, and Pineiro and Virginia linebacker Bert Krupp picked off two apiece. Oddly, there were only seven incomplete passes.

Rutgers linebacker Jim Dumont led both teams in tackles with 13; Krupp and linebacker Keith Lee had 12 each for Virginia. Rutgers stopped Virginia runners 12 times for losses.

"It was a great defensive game, no doubt about that," said Rutgers Coach Frank Burns. "But it bothers me about our offense. We just can't have the turnovers that we had. Maybe our kids were a bit anxious."

Although Rutgers remained unbeaten with its third victory, there were many boos from the crowd of 22,816 in Giants Stadium. Many were directed at quarterback Ralph Leek, particularly after he faded to pass late in the third quarter, tripped himself and fell.

"Good for the fans, tough on the coaches," said Earle Mosley, a Rutgers assistant coach, mopping sweat from his forehead.

The fans probably disagreed.