Carson, a 5-10 guard, was 9-of-16 from the field and also had nine rebounds and five assists. Marshall was 7-of-12 from the field.
Arizona State (8-2) had dropped two of its three previous games -- losses to Creighton and Miami (Fla.) -- after starting the season by winning six straight.
The Sun Devils led by just three points at halftime (28-25) before taking control in the second half.
Billy Garrett led DePaul with 14 points, but the Blue Demons struggled offensively throughout the game, going 19-of-65 for a season-low 29.2 percent.
DePaul (4-4) was coming off its most impressive win of the season, a 93-81 victory over Oregon State last Sunday.
DePaul was playing without point guard Brandon Young, who sat out because of an ankle injury. Young is the team's assists leader and second-leading scorer (16.3 points) and the Blue Demons appeared unsettled without their leader early on.
DePaul didn't record its first field goal until nearly five minutes had expired when Garrett scored on a layup with 15:13 left in the first half.
Arizona State, though, had its own offensive issues early. Although the Sun Devils led throughout the first half, they were never able to open a significant lead despite the fact DePaul made just 10 of 36 shots (27.8 percent), including 1-of-11 from three-point range.
Cleveland Melvin, the Blue Demons' leading scorer, was scoreless in the first half, missing all seven of his field-goal attempts.
Still, Arizona State only led 28-25 at halftime.
DePaul got off to another sluggish start in the second half, but this time the Sun Devils capitalized to take command. They scored the first four points of the half for a 34-25 advantage and a few minutes later stretched their advantage to double digits (45-34) for the first time on a basket by Shaquielle McKissic.
Following a DePaul basket, the onslaught continued as ASU hit a three-pointer on its next three possessions -- the first two by Marshall -- to give it a 54-36 edge with 12:02 to play. The lead reached 20 points (56-36) on a basket by Eric Jacobsen on the next possession.
The difference in the surge was shooting. The Sun Devils started knocking down shots with uncanny regularity, while the Blue Demons continued to struggle. With the score 61-41 with just under eight minutes left, ASU was 11-for-16 (68.8 percent) from the field in the second half (including 3-of-5 on three-pointers) and DePaul was 5-of-19 (26.3 percent).