The New York Giants keep talking about how they want to climb higher on the ladder of prestige.

This seems strange, since they now sit with Dallas on the top rung of the NFC East, a canary singing on their shoulders.

Today, the Giants recovered from a 13-point first-half deficit to defeat the Los Angeles Rams, 24-19, before 74,663 at Giants Stadium.

"A couple years ago," said Giants linebacker Harry Carson, "it would have been over for us at halftime. But now we've got a team of talent and willpower."

"The only time you used to hear about the Giants," New York receiver Lionel Manuel said, "was when somebody was talking about (linebacker) Lawrence Taylor. This year, it's different. People know us. They realize we're as good as anyone else."

Forgive the Giants (7-3), tied with the Cowboys for first place and heading to RFK Stadium to play the Redskins next Monday night. They are on the move and hold a sassy 5-1 mark against division teams, the most important number, come tie-breaker time.

The Giants are in the middle of a four-game winning streak, and their last four-game streak came way back in 1979.

Scratch out the York, they say. Just New Giants. "Too bad this wasn't a championship game," Manuel said.

The Giants' victory combination today mixed controversy with cool. The New York defense limited the Rams to one touchdown, on a six-yard drive that followed a first-quarter fumble by Manuel.

Furthermore, with the Rams' starting quarterback, Dieter Brock, sidelined after having kidney stones removed last week, replacement Jeff Kemp had fits. The congressman's son from Churchill High made his first start of the season and completed only 10 of 25 passes, and running back Eric Dickerson (101 yards) couldn't escape for more than 12 yards on any run.

In the end, though, the Rams (8-2) were muttering about two referees' decisions in the fourth quarter that allowed the Giants to expand their 17-16 edge.

The Giants, who trailed by 16-7 early in the third quarter, built that edge when Eric Schubert kicked a 40-yard field goal, when the Los Angeles offensive line committed various atrocities (two penalties and little protection for Kemp) and when Giants quarterback Phil Simms capitalized on a poor punt by Dale Hatcher.

Simms hit several key passes to arrange for running back Joe Morris' one-yard scoring run and the one-point lead.

"They made the big plays on us like other teams haven't done," Rams Coach John Robinson said.

The controversy came early in the fourth quarter for the Rams, whose only previous loss was to the San Francisco 49ers, who, with a win Monday night over Denver, can pull within two games of the Rams in the NFC West.

The Giants first benefited from a 39-yard pass-interference call against cornerback LeRoy Irvin, who brushed against receiver Bobby Johnson on an underthrown pass at the Rams' four.

The Rams and Irvin argued that the ball was not catchable. Johnson later said he could have caught it. Field judge Bill Stanley said, "(Irvin) clearly bumped the receiver before the ball got there. The receiver was definitely looking at the ball; the defender wasn't."

Moments later, Morris ran three yards for a touchdown that expanded the Giants' lead to 24-16 with 11:01 left.

The Rams didn't streak to 8-1 for nothing. They are resourceful, although today's game again proved that their defense is their strength.

After Morris' score, the Rams' Ron Brown, a sprinter who won a gold medal in the Olympics, took the ensuing kickoff 89 yards, to the Giants' 11.

On third down from the eight, Kemp threw to receiver Bobby Duckworth, who made the catch with arms raised and dragged one foot in bounds in the end zone before safety Kenny Hill knocked him out of bounds. The play was ruled incomplete.

The NFL rule book specifies that a receiver must get two feet in bounds for a completion and, if a defender knocks a receiver out of bounds who otherwise would have been in bounds, it becomes a judgment call for the official.

Rams Coach Robinson dashed down the sideline, screaming at officials. Duckworth lay prone, having suffered a shoulder injury. Later, back judge Tom Kelleher said, "Even without the defender, my judgment says (Duckworth) couldn't have stopped and gotten the second foot in bounds."

The Rams settled for Mike Lansford's fourth field goal, this from 25 yards, to pull within 24-19 with 9:14 to play.

The Los Angeles offense failed twice more. On the first drive, tight end Tony Hunter dropped a potential 35-yard gain near the Rams' 35, even though he was wide open.

Finally, safety Hill intercepted a deflected pass by Kemp at the Giants' 48 with 13 seconds to play. End of Rams.

"Obviously, not getting the touchdown to Duckworth hurt us. If we had gotten that (to pull within 24-23), we could have played for a field goal," said Robinson. "I did not have a complete view of the calls. I thought the calls were controversial . . . I moaned at the time, but it didn't do any good."

The Giants said they were more concerned about Kemp's ability to run (four carries for two yards) than his ability to pass (130 yards).

Simms was booed throughout. George Young, the Giants' general manager, said, "I went to the World Series at Yankee Stadium in 1942 and heard them boo Joe DiMaggio. In Baltimore, they used to boo Johnny Unitas for three quarters, then carry him off the field. Fans are that way."

Kemp said he was pleased with his performance. He left Giants Stadium late today with his father, U.S. Rep. Jack Kemp (R-N.Y.), a former NFL quarterback himself. "Good job, young man. I'm really proud of you," the father said. The son just shook his head and gave a weak smile.