Horactio Banks had 13 carries for 134 yards for the Cardinals (1-0). KeVonn Mabon finished with 11 receptions for 110 yards and a touchdown.
Ball State led 13-0 early in the second quarter as Scott Secor kicked two field goals and Mann found Mabon for a 34-yard score in between.
Colgate (0-1) cut the deficit to six with a 4-yard touchdown run by James Travellin. Mann responded with a late 19-yard touchdown pass to Aaron Hepp, giving Ball State a 20-7 halftime lead.
Edwards added some cushion for the Cardinals with a 4-yard score in the third quarter.
Mann finished 20 of 32 for 203 yards with an interception.
Colgate converted just 2 of 13 third downs while John Quazza had six catches for 92 yards.