Even the New York Giants, who for 18 years have been among the worst teams in the National Football League, couldn't blow this one.

Although the Philadelphia Eagles rallied from a 20-0 first-quarter deficit, the Giants still salvaged their first playoff victory since 1958 by simply giving the ball to halfback Rob Carpenter, whose fourth-period running enabled New York to come away with a stunning 27-21 victory in this NFC wild-card game.

In the process of knocking out one of the 1981 Super Bowl finalists, the Giants borrowed strategy from Eagle Coach Dick Vermeil, who built Philadelphia into a powerhouse by combining a highly physical offense with a simple, aggressive defense.

Today, it was the Giants who controlled things with Carpenter's ball carrying (career-high 161 yards on 33 carries) and a quick defense that almost let the Eagles come back--but not quite.

Now New York has a week to prepare for Sunday's NFC semifinal game at San Francisco against the even more surprising 49ers, who beat the Giants, 17-10, a month ago.

This New York team has improved since then, however. Winners of five of their last six, the Giants are growing stronger as their offense, especially Carpenter and quarterback Scott Brunner, matures to take pressure off that wonderful defense.

Never was that more evident than today. The Giant offense, last in the league statistically, took advantage of every break presented by Philadelphia in the first half. And then in the second, when the Eagles were starting to get their offense going, New York gained two vital first downs without needing to pass, preventing Philadelphia from touching the ball one last time.

"The defense has been given credit for getting us here," defensive end Gary Jeter said, "but I think the offense showed what it could do today. When we needed them to do something in the fourth period, they did. I just didn't want the Eagles to get the ball back and they didn't."

The Eagles' memories of this one will be largely of the opening quarter, not those final few minutes. They made enough errors to help out any opponent, but they were especially harmful against a Giant defense that is at its best with a substantial lead.

The early New York points came quickly. On the game's opening series, the Giants had to kick, only to regain possession when Wally Henry fumbled the punt after a hard hit by Lawrence Taylor. New York recovered on the Eagle 23 and scored moments later on a swing pass from Brunner to halfback Leon Bright. Joe Danelo's conversion was blocked and the Giants led, 6-0.

"I didn't think I had enough room to catch the ball," Henry said. "Lawrence Taylor came in there and hit me before I even had touched the ball. He just knocked me away from it."

After an Eagle punt, New York drove 63 yards on 11 plays, with Brunner, a second-year man from Delaware, completing four passes, including a 10-yard scoring toss to John Mistler for a 13-0 advantage with 6:46 gone.

Then came the game's pivotal play. Henry drifted to his right on the ensuing kickoff after at first thinking Booker Russell would handle it. The ball went through Henry's arms and, when he tried to pick it up, he was smashed by Mike Dennis. The ball bounded into the end zone, where Mark Haynes recovered it for another touchdown just 12 seconds after Mistler's score.

An exchange of touchdowns had the Giants ahead, 27-7, at the half and then it became a matter of whether New York, in its first playoff game since 1963, could hang on. The Eagles drove 82 yards with the third-quarter kickoff for one touchdown and got a second with 2:51 left in the game, with the help of three major penalty calls on the Giants.

New York turned again to Carpenter, who was obtained from Houston for a third-round choice a month into the season. In the second half, he already had carried on 12 of the Giants' 14 plays (and caught a pass on another), including eight in a row against the NFC's No. 1 defense. The Giants didn't want to throw the ball or do anything that could be turned into a game-winning mistake by Philadelphia.

"I wasn't tired," Carpenter said. "They kept giving me the ball and I kept running with it. I'd do that all day if they'd let me."

Carpenter had been running mostly behind the blocking of center Jim Clack, who had returned from retirement at midseason and now was manhandling all-conference middle guard Charlie Johnson. But at the end, Carpenter relied three straight times on the blocking of tackle Gordon King. Using a play the Giants call "ride 14," Carpenter gained six yards, then three, then five more for a first down with 88 seconds left. Carpenter finished his performance with a 14-yard run off left tackle.

The Eagles couldn't stop the clock any more, and, after two keepers by Brunner, time ran out on Philadelphia.

"This is the greatest day of my football career," said Carpenter, who had been a fill-in at Houston behind Earl Campbell. "There was the day I was born, the day I got married and then today. The best thing that has ever happened to me is when I got traded to the New York Giants."

Remarkably, the Giants did most of their work on the ground by going straight at the Eagles, which usually is all but impossible. Nothing fancy involved, just one-on-one blocking with Carpenter reading his line and picking his holes. Philadelphia knew what was coming, everyone in Veterans Stadium did, yet Carpenter succeeded.

"It got to a point," Carpenter said, "that I knew what my line was going to do before they even did it. On that drive in the second quarter (when Carpenter carried four times for 40 yards to set up a touchdown), the feeling was unbelievable."

The feeling Giant fans have after this triumph must be equally unbelievable. Their team has had only two winning seasons since 1963 and finished 4-12 last season. And 11 games into this season, after losing to Washington in overtime, New York was 5-6.

But following last week's overtime victory against Dallas and this impressive showing today, the Giants no longer are a joke.

"I've been around when it was hard to hold up your head," said Jeter. "Now it's fun to say I'm proud of what we have accomplished."

Jo Jo Heath, an Eagle special-teamer, was carried off the field on a stretcher late in the game following a Philadelphia punt. His injury was diagnosed as a jammed neck and he left the locker room without aid.