Saquon Barkley took the handoff and angled to his right.

Then he saw the cutback lane.

And he was gone.

The rookie has hurdled men standing almost straight up this season. He has broken ankles with his cuts. He has stiff-armed defenders into submission.

And Sunday, he displayed his pure speed.

He cut left near the line of scrimmage and sprinted untouched for 78 yards to score his franchise rookie record 13th touchdown. It set the tone in a 40-16 demolition of Washington at FedEx Field.

Barkley rushed for 170 yards on just 14 carries — he didn’t play in the fourth quarter — in leading the Giants (5-8) to their best performance of the season and their fourth win in five games.

It was such a blowout, rookie quarterback Kyle Lauletta made his NFL debut, replacing a sharp Eli Manning (14-of-22 passing, 197 yards, 3 TDs, 0 INTs) to start the fourth quarter.

And the Giants did it without Odell Beckham Jr., who was sidelined by a bruised quadriceps.

In a season where little had gone right in the first eight games, there was always Saquon.

He is the embodiment of hope. And now, he just might be the face of the franchise.

Barkley surpassed 1,000 rushing yards for the season on the touchdown run to become the first Giants rookie to reach the milestone. It was his fifth touchdown of 50 or more yards. It gave the Giants a 17-0 lead with 8:42 remaining in the second quarter.

And it was only the beginning.

The 5-foot-11, 233-pound running back finished the first half with 159 yards on 10 carries. It included a 52-yard run late in the second quarter, highlighted by a wicked stiff-arm to Josh Norman that set up the Giants at the Washington 6-yard line.

It resulted in Manning’s 6-yard touchdown pass to Bennie Fowler, giving them a 31-0 lead with 1:48 remaining in the first half.

The Giants rode a 27-point second quarter to take a 34-0 lead into the halftime locker room.

Barkley surpassed 100 rushing yards for the fourth game in a row and the sixth time this season — the most by a rookie in team history.

He also recorded a one-handed reception in the third quarter and finished with four catches for 27 yards.

Barkley recorded 100 yards or more of offense for the 12th time this season. Only Hall of Famer Eric Dickerson had more as a rookie (13).

Barkley also became the first Giants running back since Ahmad Bradshaw in 2012 to rush for 1,000 yards in a season.

The Giants scored 40 points or more for the first time since Nov. 1, 2015 (a 52-49 loss in New Orleans) in winning their first game over an NFC East opponent.

“I like the locker room. I think the guys are listening,” coach Pat Shurmur said. “We’re on the right track.”

Moments that mattered

Barkley dazzles, Part 1: Barkley broke a 78-yard run untouched for a touchdown with 8:42 left in the first half to give the Giants a 17-0 lead.

Barkley dazzles, Part 2: Barkley broke a 52-yard run to set up Manning’s 6-yard scoring pass to Fowler for a 31-0 lead with 1:48 remaining in the first half.

The Mann: Manning hit Russell Shepard with an 11-yard touchdown pass — Manning’s third of the game — to give the Giants a 40-0 lead with 5:38 left in the third. Surprisingly, Aldrick Rosas missed the point after attempt.

Engram returns: TE Evan Engram made his presence felt in his return from a hamstring injury that sidelined him two games, producing a 39-yard catch and run play that resulted in Rosas’ 23-yard field goal as the first half ended. It gave the Giants 34-0 lead. He finished with three receptions for 77 yards.

Shutout broken: The Giants held Washington (6-7) scoreless until 11:56 remained in the game when quarterback Josh Johnson — who replaced Mark Sanchez in the third quarter — ran it in for an 8-yard touchdown run.

The Redskins added another when Johnson found Jamison Crowder for a 79-yard touchdown with 8:48 remaining.

Pick-Six: Curtis Riley gave the Giants their first points with 2:45 remaining in the first quarter when he intercepted a tipped pass from Sanchez and walked it in for a 9-yard touchdown return.

James Bettcher’s defense has produced a pick-six in three of its past four games — the other two by Alec Ogletree. Kareem Martin tipped the pass, and Riley hauled it in for his third interception of the season.

Pick to points: Ogletree intercepted his fifth pass of the season in the second quarter, returning it 18 yards and setting up the Giants at the Washington 10. It came on another tipped Sanchez pass, this one deflected by Tae Davis.

It resulted in Manning’s 3-yard touchdown pass to Sterling Shepard, giving the Giants a 24-0 lead with 6:21 remaining in first half.

Breaking in: Lauletta was intercepted by Mason Foster on his second NFL pass. His first was an incompletion. He finished 0-for-5 passing. [Full story]

Injury news

There appeared to be no noteworthy injuries for the Giants.

What’s next?

The Giants host the Tennessee Titans (7-6) next Sunday at 1 p.m. ET. The Titans are coming off a 30-9 whipping of Jacksonville, in which RB Derrick Henry rushed for a franchise record 238 yards and four touchdowns. Tennessee will be rested, having played on Thursday night. And the Titans probably will be focused — still competing for an AFC wild card.