Davis, a rookie out of Clemson, racked up 116 yards on 12 carries for Cleveland, including an 81-yard touchdown run in the third quarter.
The Browns scored quickly as Lewis barreled into the end zone for a 4-yard TD to complete the opening drive of the game.
Lions quarterback Matthew Stafford, the top draft pick, struggled from the start, as his first pass got picked off by Browns cornerback Eric Wright. Stafford went 5-of-13 for 34 yards. His veteran teammate, Daunte Culpepper, by contrast, completed 10-of-16 for 86 yards.
After Wright's interception, the Browns' Phil Dawson hit a 33-yard field goal.
Joshua Cribbs returned a punt 84 yards for a TD midway through the first quarter, giving the Browns a 17-0 lead, and a second field goal made it 20-0.
The Lions' Swayze Waters kicked a field goal from 51 yards out near the end of the first half.
Third-string Lions quarterback Drew Stanton connected on a 20-yard TD pass to Carson Butler in the third quarter.