Best's third-quarter score was the second-longest run in Lions' history and gave Detroit a 21-10 lead.
Matthew Stafford completed 19-of-26 passes for 219 yards and a pair of touchdowns while yielding an interception for the Lions (5-0), one of only two remaining undefeated teams in the NFL. The other is NFC Central rival Green Bay.
Calvin Johnson made five grabs for 130 yards, including a 73-yard scoring strike in the second quarter as the Lions continued their best start since the 1956 team, which won six straight to begin the season.
Jay Cutler went 28-of-38 through the air for 249 yards with a TD and no interceptions for Chicago (2-3), which has lost to both Green Bay and Detroit this season.
Matt Forte carried the ball 22 times for 116 yards for the Bears.