By the time the New York Giants' 27-17 victory over St. Louis was finalized at Giants Stadium today, no one seemed to remember that this kind of thing wasn't supposed to happen to these Cardinals.

St. Louis began the day as the 2-0 viceroys of the NFC East, having scored 68 points in two NFL games. The latest version of the Offense of the Eighties, it seemed, flourished under the Gateway Arch. Neil Lomax to Roy Green was like having Aladdin in a bottle. Today, however, the Giants defused the St. Louis offense and brought themselves back into a 2-1 first-place tie in the NFC East with the Cowboys and the Cardinals.

"If we had lost this one," said Giants receiver Bobby Johnson, who caught two touchdown passes, "we would have been deep, deep down."

The Giants' defense limited wide receivers Green and Pat Tilley to a total of one catch and held the Cardinals' runners to 83 yards. The Cardinals were zero for nine in third-down conversions and were burdened further by 10 penalties.

When Lomax, the all-pro quarterback, threw a 15-yard scoring pass to fullback Earl Ferrell for the game's final points with less than five minutes to play, the stadium was half empty and the Jersey Turnpike was filling up fast.

"Just leave it this way, when all was said and done for us, more was said than done," said Green, whose one catch was a 39-yarder that tied the game at 7 late in the first quarter.

St. Louis Coach Jim Hanifan: "Gee whiz, our offense self-destructed."

Meanwhile, Giants quarterback Phil Simms made the most of his 10 completions, throwing three touchdown passes, two to Johnson and one to a former Navy player Phil McConkey. Before today, neither Johnson nor McConkey had caught a pass.

The Giants' running game expertly deployed its aces. Joe Morris darted for 85 yards. Rookie George Adams converted two key short-yardage plays. Maurice Carthon threw several key blocks. Tony Galbreath had 123 yards worth of runs (27), catches (40) and kick returns (56).

Even the forgotten one, fullback Rob Carpenter, ran 23 yards on the scoring drive that sealed it at 27-10 early in the fourth quarter. The Giants finished with a Cardinals-breaking 155 yards rushing.

The Giants' special teams gave the final touch to this day of precision. Sean Landeta, formerly of the USFL Baltimore Stars, punted five times for a 49-yard average. And Jess Atkinson, the former Maryland kicker whom the Giants signed last week to replace injured Ali-Haji Sheikh, converted two of three field goal tries in his pro debut.

Atkinson made gimmes from 20 and 19 yards and missed wide right from 49 yards in the second quarter when the Giants' lead was a tenuous 13-10.

Quite relieved that his miss didn't matter in the end, he said: "On the 19-yarder I made, I was aiming at a big, bald dude in a yellow shirt in the upper deck."

"This was like a swing game for us," said Lawrence Taylor, the Giants' defensive dominator. "After that (23-20) loss to Green Bay last week, we were doubting ourselves a little. This is like another chance for us now."

Lomax finished 18 of 34 for 234 yards. But only two of his passes went to wide receivers, a percentage that is becoming too common for the Cardinals. Tilley has caught only one pass in three games.

Len Fontes, the Giants' defensive backfield coach, said the strategy was simple. The Giants played 75 percent zone, 25 percent man-to-man and, every time the Cardinals went to the shotgun, Green was double-covered. Allow the short passes, but nothing deep, Fontes told his defensive backs.

The Cardinals, after a 10-10 tie at the half, began the third quarter by committing three penalties on their first drive. The last one negated a punt downed at the Giants four. Forced to rekick, Carl Birdsong punted into the end zone for a touchback and a 16-yard advancement for New York.

It made a difference. Mixing Morris runs with short passes, the Giants drove to third and goal at the Cardinals two. However, Simms bobbled the snap and had to fall on the ball. So the Giants settled for Atkinson's 19-yard field goal and a 13-10 lead with 3:40 left in the third quarter.

Three plays later, St. Louis running back Stump Mitchell was hit hard on a short-yardage play by linebacker Gary Reasons and fumbled. The Giants took possession at the St. Louis 22. The Cardinals were left to bemoan the fact that running back Ottis Anderson sat out much of the second half because of an eye injury.

Forty-nine seconds after the fumble, McConkey beat cornerback Wayne Smith on a simple down-and-in pattern for a 20-yard touchdown. "I'm just doing things that I know I can do," McConkey said later. The Giants led, 20-10, and the Cardinals were letting the game slip away.

It slipped away for good on the first play of the fourth quarter when Lomax overthrew Ferrell and safety Terry Kinard intercepted at the Giants 35. Kinard returned 17 yards to the 48. This spawned a six-play drive that finished with Simms, out of the shotgun, passing to Johnson for a 16-yard touchdown.

And so, once again, the Cardinals lost a game that might have established them as a verifiably elite NFL team.

Lomax said: "Everybody keeps talking about how great we are. I haven't seen it. We were 9-7 last year and lost to Washington. We haven't made the playoffs in a couple years (most recently in strike-time 1982)."

"The last couple of years, we've been one game away," Green said. "If I knew the answer, I'd spread the word around the locker room."