Coleman, who was 18 of 31, scored the first touchdown for the Mocs (4-1, 2-1 Southern Conference) on a 1-yard run with 6:31 left in the first quarter.
Chris Pitchford had five passes for 135 yards for Chattanooga, which is 4-1 for the first time since 1997. The Mocs also opened the season 2-0 on the road for the first time since 1980.
Chris Awuah, who finished with 40 yards rushing, scored on a 1-yard run with 9:40 left in the first half for a 14-0 Chattanooga lead.
Dustin Taliaferro put the Bulldogs (3-3, 1-2) on the scoreboard with a 1-yard run with 9:52 left to play.
Samford was led by Taliaferro, who was 25 of 31 with 165 yards and one interception.