New York Giants wide receiver Darius Slayton (86) is unable...

New York Giants wide receiver Darius Slayton (86) is unable to catch a pass in front of Dallas Cowboys cornerback Josh Butler (31) during the first half of an NFL football game in Arlington, Texas on Thursday. Credit: AP/Tony Gutierrez

ARLINGTON, Texas — The Giants discovered a new layer of despair Thursday, and if their 27-20 loss to a wholly unremarkable Cowboys team is any indication, they face five more miserable weeks of plunging into the depths of their own inadequacy.

Part of a Thanksgiving Day slate that generally is one of the most-watched NFL events of the regular season, the Giants proved to a large national audience that the problem isn’t just the quarterback . . . or the play-calling . . . or the defense.

It’s everything.

And because things apparently can always get worse, they also lost defensive lineman Dexter Lawrence to a dislocated elbow in the third quarter. Lawrence did not know if it’s a season-ending injury.

With Tommy DeVito sidelined with a right forearm injury and Drew Lock under center, the Giants (2-10) managed only 247 yards of total offense en route to their seventh straight loss this season, eighth straight loss to Dallas (5-7) and eighth straight loss at AT&T Stadium.

The only bright spot was barely that: a first-quarter touchdown granted them their first lead since Week 6, though even that lasted only 6:36. They committed 13 penalties for 98 yards.

“Disappointing trip,” coach Brian Daboll said. “Some [penalties] are physical, but the other ones, the pre-snap ones, you have to do a better job of that ... Today, it was a couple turnovers and there were certain plays that we had opportunities to either make or call or whatever it may be, but just not good enough.”

The Giants did draw to within a touchdown with 2:18 left in the game on Lock’s 8-yard scoring run, but Cooper Rush’s third-down conversion on a 3-yard pass to Brandin Cooks sealed it.

“I came into this excited to show what I could do,” said Lock, who said he heard he might be starting right before the Giants departed for Texas. “This is one of my first times being able to come in and play a full game with these guys and show them what I can do, minus the turnovers and a few things. It was up and down.”

Lock was 21-for-32 for 178 yards and an interception, plus the rushing touchdown and an earlier 28-yard run.

That standout play came on the Giants’ first score: On third-and-6 from the Dallas 29, Lock was flushed from the pocket on a blitz, took off in the open field and nearly scored after a massive block by Darius Slayton at the goal line. Though it originally was ruled a touchdown, Lock kicked the pylon and fell out of bounds to put the ball at the 1. Tyrone Tracy Jr. punched it in on the next play to give the Giants a 7-3 lead with 3:06 left in the first quarter.

That, though, was before they gave up a field goal and a touchdown in the span of 15 seconds.

A facemask penalty left the Cowboys at second-and-21 on their own 32 late in the first quarter, but Rico Dowdell (112 yards, 22 carries) broke through the middle on a draw for a 22-yard run, the longest by a Cowboys running back this season. They made it as far as the Giants’ 15 before Rush’s pass intended for CeeDee Lamb fell incomplete, and the Cowboys kicked a 33-yard field goal to draw within 7-6. (Rush, also a backup, started in lieu of Dak Prescott, who went down with a hamstring injury in Week 9.)

Despair wasn’t done with the Giants, though — not even close. On first-and-10 at his own 40, Lock attempted a screen pass to Devin Singletary, but DeMarvion Overshown beat Singletary on the blitz, reached up to deflect the throw, caught his own deflection and took it 23 yards for a pick-6 and a 13-7 Cowboys lead.

The Giants got to 13-10 with 3:21 left in the half on Graham Gano’s 46-yard field goal but squandered an opportunity minutes later when, on third-and-15 at the Cowboys’ 36, Mike McCarthy called a fullback draw with Hunter Luepke for a gain of just two yards, prompting hefty boos from the crowd and giving the Giants the ball back at the two-minute warning with three of their timeouts remaining. They did nothing with it, though, going three-and-out in 14 seconds.

It continued to devolve. The Giants went three-and-out to kick off the second half but looked to finally catch a break on the Cowboys’ subsequent drive when Rush appeared to fumble near the goal line, a play that was ruled a touchback when Micah McFadden recovered the ball in the end zone.

A replay, though, showed that Rush went down at the 2-yard line before losing control of the football. The Cowboys retained possession and, on the next play, Rush hit Cooks with a scoring pass to give the Cowboys a 20-10 lead with 11:37 left in the third quarter.

The Cowboys then scored on a nine-play, 70-yard drive capped by Dowdle’s 4-yard run off right guard.

Gano kicked a 47-yard field goal with 13:34 left in the game to get the Giants to within 27-13. Lock capped an eight-play, 80-yard drive with an 8-yard touchdown run with 2:18 left to make it a one-score game.

“We’ve got to get some wins,” Malik Nabers said. “We’ve got a few games left and we’ve got to figure out how to pull some Ws through ... It was important that we continue to fight through four quarters and don’t give up, but there’s a lot of stuff we have to clean up.”