Dallas hopes to sign off on its first home victory this season

Eli Manning had his “signature” victory at the new Cowboys Stadium. This season’s Dallas Cowboys are still looking for theirs.

The 1-4 Cowboys, whose season is slipping away, play host to the New York Giants on Monday night in a critical NFC East matchup. Only five teams since 1990 have made the playoffs after losing four of their first five games.

It’s the first trip back to Arlington, Texas, for the Giants since the inaugural game at the new stadium last season, when they won, 33-31, and Manning — without permission — autographed the wall in the visitors’ locker room. He wrote his name, the date, the score, and “First win in the new stadium.”

That wall should have at least a couple of more autographs on it from this season, seeing as the Cowboys have yet to win at home and have already lost there to Chicago and Tennessee. Their only victory has come on the road, at Houston.

Despite significantly outgaining the 1-3 Minnesota Vikings last Sunday, the Cowboys made a slew of mistakes — among them having two passes intercepted and allowing a kick return for a touchdown immediately after halftime — and wound up losing the so-called Desperation Bowl.

After the game, Cowboys owner Jerry Jones said he plans to stick with beleaguered Coach Wade Phillips this season but conceded he’s not too optimistic about what’s unfolding.

A day later, Jones sounded more upbeat.

“I believe in these guys, I believe in the coaching staff, I believe in Wade Phillips,” Jones said. “I believe we can turn things around. While the odds are against us, we can make all the things happen that we wanted to do this year.”

The Giants, who looked lost earlier this season, have won three in a row and have ramped up the defensive pressure, limiting opponents to an NFC-low 264.8 yards per game.

Defensive end Osi Umenyiora has led that resurgence, even though he’s battling a knee injury that has limited his practice time. Over the last three games, he has had seven sacks and six forced fumbles.

“Osi has played well and he’s made up his mind to play well,” Coach Tom Coughlin said. “What he brings to the table in terms of his ability, his conviction, his desire to be the very best that he can be, that’s where he is. He’s an excellent football player playing very well.”

That’s not good news for Tony Romo, who is playing behind a patchwork offensive line and has had five passes intercepted in the last two games. He’s coming off a season in which he had nine passes intercepted — the first time he finished in single-digit interceptions as a starter — but he already has seven with 11 games to go.

sam.farmer@latimes.com