Brown finished with 54 rushing yards on 14 carries as the Colts (8-4) rebounded from a 40-11 loss in Arizona last week, picking up their fourth win in six games overall.
Andrew Luck completed 17-of-32 passes for 200 yards and one interception for Indianapolis.
The Titans (5-7), meanwhile, fell for the third time in four games as Ryan Fitzpatrick was limited to 201 passing yards with a score and was picked off three times.
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