Quarterback Lamar Jackson threw three touchdowns and had 103 yards on the ground as the Ravens won their 11th straight game.
Two completions to Mark Andrews – one from 39 yards and another from 14 – within just over a minute at the end of the second quarter put Baltimore up 14-6 at half-time and the defeat saw the Browns' slim play-off hopes ended.
A trio of touchdowns from Drew Brees saw the New Orleans Saints maintain their push for the NFC top seed.
The Saints saw off the Tennessee Titans 38-28, with Alvin Kamara rushing for two TDs in the third quarter for New Orleans.
Jones knocked down a deep Dak Prescott pass in the fourth quarter to deny the Cowboys a win which would have seen them take the division title.
Elsewhere, the Cincinnati Bengals scored two touchdowns within 30 seconds to force overtime against the Miami Dolphins but went on to lose 38-35, while the New York Giants sealed an overtime victory over the Washington Redskins 41-35 with Daniel Jones throwing for five touchdowns.
Nyheim Hines scored on two punt returns as the Indianapolis Colts breezed past the Carolina Panthers 38-6, the Atlanta Falcons beat the Jacksonville Jaguars 24-12 while the New York Jets were victorious over the Pittsburgh Steelers 16-10.
Kenyan Drake rushed for two scored as the Arizona Cardinals saw off the Seattle Seahawks 27-13, the Oakland Raiders beat the Los Angeles Chargers 24-17, the Denver Broncos scored 14 in the final quarter to beat the Detroit Lions 27-17 and the Kansas City Chiefs defeated the Chicago Bears 26-3.