Antone Smith's 46-yard scoring run in the third period put Atlanta in front 10-3 and the Falcons appeared ready to add to the advantage. A short pass by John Wilson, however, was picked off by Brown and he went the distance for the score that allowed the Ravens to end the exhibition season at 3-1. It was one of two interceptions thrown by Wilson.
Billy Cundiff added two field goals and Damien Berry scored for Baltimore on a 5-yard run with 2:32 to play in the game.
Smith, who has only one regular-season carry in his first two years with Atlanta, gained 114 yards on 11 carries and caught two passes for 44 yards.
Baltimore's Hunter Cantwell was 13-of-28 for 111 yards and an interception. Wilson completed 16-of-33 for 146.
The Ravens begin the regular season at home against Pittsburgh. Atlanta, winless in the pre-season, will open on the road against Chicago.