Dumervil also forced a fumble as the Broncos (2-0) caused three turnovers and bottled up Brady Quinn.
"Man, that was amazing. You don't see a guy get four sacks in one half," Davis marveled. "He really turned it on."
The entire defense did, limiting the Browns, who have scored just one touchdown in their last 33 quarters, to 200 yards of offense, just 56 of that on the ground.
The Broncos, who beat Cincinnati last week on Brandon Stokley's 87-yard touchdown catch with 11 seconds left, are unbeaten under new coach Josh McDaniels, who worked with Browns coach Eric Mangini in New England. Mangini's new team is 0-2.
Despite appearances, Dumervil said he's still a work in progress in the Broncos' new 3-4 scheme.
"Yeah, I guess I'm a linebacker now," he said. "It's fun, though. I get to play linebacker and I still get to do what I love -- rush the passer. I've found my niche. ... It makes me a complete player."
Dumervil said he has a long way to go to feel comfortable in the 3-4, but it's proving the perfect fit for this unorthodox player who has long arms for a man who stands just 5-11, as Pro Bowl tackle Joe Thomas saw over and over Sunday.
"You are reaching for him but he can get his hands on you first and he's got leverage and he can get underneath you and just push you back to the quarterback," McDaniels said. "His skills set is pretty much alone in this league."
So, Dumervil often finds himself standing over a crumpled quarterback with a big lineman sprawled out behind him.
"I've been going through it all my life," Dumervil said. "It's easy for me. I have instant leverage, I guess."
Quinn finished 18 of 31 for 161 yards and an interception on his final toss.
"They're tough," Quinn said. "Across the board they have a lot of talent. Schematically, they do a good job game-planning."
Denver quarterback Kyle Orton, who completed 19 of 37 passes for 263 yards and a touchdown, was having another ordinary day until he hit Jabar Gaffney with a 49-yard pass that led to Peyton Hillis' 2-yard TD run early in the fourth quarter.
That broke open a 13-6 game and atoned for Hillis' lost fumble on the opening kickoff.
Running back Correll Buckhalter then broke free for a 45-yard touchdown rumble that made it 27-6.
Asked if he was tempted to bench Quinn, who's been sacked nine times already, in favor of Derek Anderson, Mangini said: "What I'm looking to do is play better across the board."
"The offense had nothing to do with the two long defensive plays," Mangini said of Gaffney's big catch and Buckhalter's big run. "That's a risk you take when you blitz."
Before the Broncos' offense picked up steam, the crowd booed Orton for some badly thrown passes on a windy day at Invesco Field and jeered kicker Matt Prater, who missed from 37 and 39 yards but was good from 23 and 38.
The defense was the only unit that wasn't erratic. In two games, the Broncos have allowed just one touchdown.
Providing the early spark Sunday was Davis, who had eagerly awaited facing the team that let him go after seven seasons without so much as a goodbye from its new coach.
When the Browns didn't make him an offer, Davis signed a two-year deal with the Broncos, who spent the offseason revamping a deplorable defense that ranked at or near the bottom in every major category last season and surrendered 448 points.
Davis recorded seven solo tackles and two assists in the first half.
"Andra showed up a bunch today," McDaniels said.
"Ah, man. That's one guy I thought had a great game," Dumervil said. "I think the four sacks kind of overshadowed it a little bit, but my MVP is 'Dre Davis. He's been our emotional leader since he came on board."
The Broncos led 10-6 at halftime, when former TE Shannon Sharpe, who skydived into the stadium as part of a tandem parachute jump, was tearfully inducted into the team's Ring of Honor. ... Broncos WR Brandon Marshall had three catches for 34 yards and a holding penalty. ... Buckhalter had 76 yards on nine carries. ... Dumervil's four sacks tied the mark held by several others, most recently Simon Fletcher in 1990.