The Browns lost to the Ravens for the ninth straight time, but gave Baltimore all it wanted and came close to tying the game in the final minute.
Baltimore won for the third time in four games this season. Cleveland (0-4) and New Orleans are the only winless teams left in the league.
The contest was the first this year to be worked by a full-time NFL officiating crew following an agreement reached early Thursday between league owners and the officials' union.
Referee Gene Steratore and the other six officials received a standing ovation when they walked onto the field prior to the game.
The first three weeks of the season had been marked by consistent problems involving the replacement officials, highlighted by a blown call in last Monday night's game that took an apparent win away from Green Bay and gave it to Seattle.
Thursday night's game was controversy free, but it was played in a steady rain and was marred by a violent hit to the head of Cleveland punt returner Joshua Cribbs by Baltimore's Dannell Ellerbe.
Cribbs remained motionless with his eyes closed for more than 2 minutes before finally showing signs of movement. He was eventually able to walk off the field under his own power, but did not return to action.
Baltimore had a 16-10 advantage with time running out in the third period, but the Browns had the ball and their offense had shown signs of life in the second half.
Williams put an end to Cleveland's momentum, however, by stepping in front of the intended receiver and returning rookie Brandon Weeden's pass for the key score of the game.
Cleveland stayed in the contest during the fourth quarter thanks to Phil Dawson's second and third field goals and the Browns regained the ball at their own 10 with 65 seconds left. They moved into Baltimore territory and were given a final chance when Baltimore suffered an unsportsmanlike conduct penalty following a fourth-down incompletion.
Weeden's last pass, however, sailed too high and he finished 25-of-52 for 320 yards.
Baltimore quarterback Joe Flacco threw an 18-yard scoring pass to Torrey Smith in the first period and ran a yard for a score midway through the third period. He was 28-of-46 for 356 yards.
Anquan Boldin caught 131 yards of passes for the Ravens, all in the second half.