EAST RUTHERFORD, N.J. – As befits a man who is listed at 340 pounds, Dexter Lawrence has outsized expectations for himself.

"I expect to go out there and be dominant every play and every second," Lawrence said. "That's my will and my heart that I go out and play with. I don't want to let anybody down on this team."

The Giants' sixth-year defensive tackle made that statement late Sunday afternoon following a 21-15 road victory against the Cleveland Browns, a game in which Lawrence was seemingly dominant every play and every second.

He led the Giants with 2.0 sacks and four hits on quarterback Deshaun Watson. Lawrence had three tackles, but the attention he commanded from the Browns' offensive line enabled several teammates to take a big role in stifling Cleveland's offense. The Browns rushed for only 69 yards – 43 by their running backs – and their 217 total yards were the fewest allowed by the Giants since Oct. 24, 2021. The defense hit Watson 17 times and sacked him eight times.

Lawrence was his primary tormentor, and he kept reminding Cleveland's offensive linemen of that.

How often did Lawrence say to them some variation of, "you can't block me?"

"A good bit," he said, smiling. "That's just having fun. There's nothing to that, too much. It's just let them know I'm here."

At one point, backup lineman Nick Harris came in to play guard.

"I let him know, too," Lawrence said.

Lawrence was a second-team all-pro and a Pro Bowler each of the previous two seasons and has begun this season as if he will make it three in a row. His 3.0 sacks tie safety Jason Pinnock for the team lead. Lawrence and outside linebacker Kayvon Thibodeaux are tied with a team-high five quarterback hits. He has 10 tackles (six solo), but his value extends far beyond the numbers because of the attention he demands and the disruption he creates.

"Dex is going to be a handful for a lot of guys in this league, whether it's one or two guys (trying to block him)," defensive coordinator Shane Bowen said. "He has a knack for winning versus two, which is extremely rare. If they're putting four hands on him and he's still winning, that means we've got a lot of one-on-ones on the other side. We've got to be able to win those. Hopefully, at times, that will result in maybe them having to get four hands off of him, to free him up. It goes hand-in-hand. It goes both ways. Finding ways to create for him, always, and knowing if we don't, he can still factor, is exceptional for a coordinator."

The Browns double-teamed Lawrence during much of the game yesterday and devoted additional blockers on edge rushers Brian Burns and Thibodeaux. Bowen responded by sending several other players after Watson. The Giants became just the fourth team since sacks became official in 1982 to have nine different players with at least half a sack in the same game, and the first since the Buffalo Bills in 2011.

"I think we had a great game plan," said linebacker Bobby Okereke, who had a half-sack among his eight tackles and a hit on Watson. "Shane called an aggressive game. We were getting after him (Watson). We got after him early and it was successful, so we stayed after him. Guys in the back end did a great job covering up and it was good to see a good bunch of guys get sacks."

"I loved the game plan - it helped us win," Lawrence said. "That (additional pressure) came within the game. I don't think that was the natural plan within the week. That was just adjustments that we had to do."

The defense was at its finest in the final 10 minutes of the fourth quarter, after a Cleveland touchdown and 2-point conversion cut the Giants' lead to 21-15. The Browns had three offensive possessions after that and crossed into Giants territory for just one play.

On the first series, Watson's 23-yard pass to Amari Cooper gave Cleveland a first down. But three plays later – from the Giants' 44-yard line - the quarterback lost his second fumble when he mishandled a shotgun snap and Azeez Ojulari recovered the ball.

Almost four minutes later, after the Giants' third punt of the quarter, the Browns faced a fourth-and-one at their own 29. Watson couldn't find an open receiver amid the pressure and was sacked by Lawrence for zero yards.

The Giants then had a chance to take a larger lead, but Greg Joseph missed a 48-yard field goal attempt, his first try as a Giant. That gave Cleveland yet another opportunity to take the lead. But after a first-down pass to Cooper gained six yards, the defense didn't give another inch – and Cleveland never again saw the ball.

"As a defense, we don't control exactly where the ball's going to be," Lawrence said. "And that's our understanding. We're not gonna be pissed off or down because the offense didn't move the ball during that time in the fourth quarter. You just got to respond and that's what we did. It just shows the strength of the leaders on this team and the mindset that we can continue to build."

*Coach Brian Daboll had no injury updates when he spoke to reporters on Monday morning. Because the Giants host Dallas on Thursday night, the team has an abbreviated practice schedule this week.

"We'll do walkthroughs, have a lot of meeting time, some extra meeting time, extra walkthroughs to get prepared for this game," Daboll said.

*Daboll understandably had no interest in reflecting on the Cowboys' last visit to MetLife Stadium, a 40-0 Dallas victory in the 2023 season opener.

"I think each individual person is motivated by different things," Daboll said. "And my main focus is getting ready to play this team, 2024, the team that's just played these first three games. Different players, different schemes, making sure that we're prepared. Doing a good job in our walkthroughs, in our meetings, in our communication. But our focus is on task at hand.

"We've got a short week, and we've got not much time to get ready. So that's where my focus is."

*Asked if he has concerns about Joseph, who kicked three extra points but missed his only field goal attempt, Daboll said, "We'll sit down and talk personnel stuff later today. You'd like him obviously to make that kick, he didn't. But he's done a good job when he was here in practice, and we'll talk about what we're going to do here."