Roethlisberger completed 29-of-39 passes for the RedHawks, who became the 14th Division I-A school to play 1,000 games. They have an all-time record of 612-342-44.
Roethlisberger, who went over the 7,000-yard mark in career passing, threw TD passes of six yards to Dan Tyler and 15 yards to Michael Larkin, helping Miami (2-1) build a 24-7 lead early in the third quarter.
Bradlee Van Pelt tossed TD strikes of 86 yards and 16 yards to David Anderson to pull Colorado State (2-2) within 34-21 with 4:59 left.
But Miami clinched the win on Smith's 45-yard TD run just over 1 1/2 minutes later. Smith rushed for 118 yards on 15 carries, also scoring on runs of five and 29 yards.
Van Pelt passed for 323 yards, despite completing only 14-of-24 passes. Anderson hauled in five receptions for 167 yards.
However, the Rams were held to just 39 yards on the ground on 29 attempts. Marcus Houston was Colorado State's leading rusher with just 30 yards on 11 attempts.
Miami won its first game west of the Mississippi River since 1971, snapping a five-game losing streak. The RedHawks suffered a 52-51 loss at Hawaii last season.