Defensive end George Martin returned a St. Louis fumble 20 yards for a touchdown and Rob Carpenter's 117 yards rushing included a one-yard plunge for a score today as the New York Giants beat the Cardinals, 20-10, to stay alive for their first playoff berth in 18 years.

The Giants rose to 8-7 with a home game against Dallas left. The Cardinals, a four-game winning streak snapped, dropped to 7-8 and lost any chance to qualify for postseason play as the final wild card in the NFC.

New York, which has not finished with a winning record since 1972, jumped in front to stay, 7-3, when rookie linebacker Lawrence Taylor sacked Cardinal quarterback Neil Lomax, jarring the football loose for Martin to pick up and run into the end zone. Martin had scored on a similar play in early season against the Washington Redskins, recovering a Joe Theismann fumble off a blindside sack by a Giant teammate and taking it in.

A 27-yard field goal by Joe Danelo built the New York halftime lead to 10-3, then the Giants made it 17-3 with a nine-play, 63-yard drive culminating in Carpenter's touchdown with 1:50 left in the third quarter. To wrap up his team's second 1981 victory over St. Louis, Danelo made it 20-3 on a three-pointer from 33 yards with 2:26 left.Danelo's field goals were his 100th and 101st in the NFL.

The New York defense continually frustrated Lomax, forcing three turnovers and sacking him three times for 33 yards in losses. Lomax, who had led the Cardinals to four straight victories after taking over for veteran Jim Hart, completed 16 of 31 passes for 163 yards. Scott Brunner was 12 of 24 for 86 yards for the winners.