Roberson rushed for 73 yards and helped the Wildcats turn the contest into a rout with TD runs on three successive possessions that gave Kansas State a 27-5 advantage midway through the second quarter.
Roberson also threw for 234 yards, completing 9-of-23 passes, as Kansas State (2-0) won its 37th straight regular-season game against a non-conference foe.
After allowing California to gain 440 yards last Saturday, the Wildcats held Troy State (0-1) to just 138 yards of total offense.
Troy State had a safety and took a 5-0 lead on Thomas Olmsted's 26-yard field goal with 9:13 remaining in the first quarter.
But Darren Sproles' five-yard TD run gave Kansas State the lead for good less than four minutes later.