Anderson completed 14-of-27 passes for 246 yards and threw a 3-yard scoring pass to wide receiver Donte Stallworth late in the first quarter.
Lewis gained 81 yards on 20 carries. He scored on a 2-yard, second-quarter run.
Placekicker Phil Dawson added three field goals for the Browns (3-4), who have won three of their last four after starting the season with three straight losses.
Cleveland played without suspended tight end Kellen Winslow Jr. He did not make the team flight despite having his $25,000 team fine rescinded.
Jacksonville quarterback David Garard completed 25-of-42 passes for 283 yards and two touchdown tosses.
Tight end Matt Jones had eight receptions for 117 yards with one touchdown, while wide receiver Reggie Williams scored once after three catches for 42 yards in the Jaguars' second loss in their last three outings.