Tracy Abrams added 13 points and Tyler Griffey had 10 for the Illini, who hit 10 of 18 3-pointers in the first half en route to a 43-25 lead at the break. Illinois was just 15 of 35 overall from the field in the first half but broke a tie game with a 29-11 run heading into halftime.
Murphy Burnatowski scored 23 points to lead Colgate.
Groce guided Ohio to the Sweet 16 last season before replacing Bruce Weber, who was fired as Illinois coach in March after losing 12 of the last 14 games.
Paul also had eight rebounds and five assists for the Illini.