Brady's first touchdown pass of the night was set up by Jacob Hollister's recovery of a muffed punt and it was caught by Rex Burkhead, who also blocked a punt to set up one of Stephen Gostkowski's two field goals.
Lewis also ran for a touchdown in helping the Patriots (7-2) win on the road for the 12th straight time. The streak ties a club record and is second only in NFL history to the San Francisco 49ers' record 18-game road winning streak from 1988 to 1990.
The Broncos (3-6) lost their fifth straight since a 3-1 start and struggled offensively to complete drives, settling for Brandon McManus field goals three times in the first half when punching the ball into the end zone would have allowed them to go toe to toe with the Patriots.
It was the seventh time in seven years the Patriots and Broncos have met in the regular season. New England won for the sixth time in that span.
Brock Osweiler, making a second straight start since replacing Trevor Siemian, was 18 of 33 for 221 yards, including a touchdown pass to Demaryius Thomas.
Brady completed 25-of-34 passes for 266 yards and led a masterful 16-play, 94-yard drive that ended in a 6-yard touchdown pass to James White early in the fourth quarter, basically quashing any Broncos hopes for a comeback.
Trailing by 18 points, the Broncos put together a 13-play drive that Osweiler finished with a 7-yard touchdown pass to Thomas, but the Patriots brushed off the score and went right back to work.
Brady drove the Patriots right down the field and Lewis plowed through the middle of the Denver defense for an 8-yard touchdown run and a 34-16 New England lead with 4:36 left in the third quarter.
The Patriots led 27-9 at halftime, bolstered by special teams play and two touchdown passes by Brady, including an 11-yarder to tight end Dwayne Allen with 25 seconds left in the second quarter.
The Broncos were poised to get the ball after stopping the Patriots' opening possession with a three-and-out, but rookie Isaiah McKenzie muffed the punt and Hollister recovered at the Broncos' 24-yard line.
It was the first in a slew of special teams breakdowns that were costly for the Broncos.
Two plays after the muffed punt, Burkhead got a step on safety Darian Stewart on a crossing pattern and Brady hit him in stride for a 14-yard touchdown pass.
Denver answered with the first of three first-half field goals by McManus, but Lewis broke loose for his 103-yard kickoff touchdown. He dodged Shaquil Barrett at the 20, side-stepped a diving McManus near midfield and withstood a desperation shove by Devontae Booker near the sideline, staying in bounds to finish out the scoring run.
The Patriots added another special teams impact play when Burkhead broke through to block a Riley Dixon punt, leading to Gostkowski's second field goal of the game, a 28-yarder that gave the Patriots a 20-6 lead midway through the second quarter.
NOTES: Patriots WR Matthew Slater went out in the first half with a hamstring injury. ... New England has now blocked 12 kicks since 2014 (eight field goals, two extra points and two punts), tying Baltimore and Philadelphia for most in that span. ... Broncos LB Todd Davis went out in the first half with an ankle injury. ... Allen Barbe started at right tackle for Denver in place of Menelik Watson, who went on injured reserve last week.