Mueller completed 29-of-37 passing attempts for 330 yards and two touchdowns to help the Rams improve to 3-1.
Kolten Solomon caught two TD passes while Michael Kiapway added two more rushing scores.
Elsewhere, No. 4 Laval won a laugher, 69-0 over McGill.
At Saskatoon, Solomon caught his first TD but a rouge and a touchdown pass to Kit Hillis gave the Huskies (2-2) an 8-7 lead in the first quarter.
Both teams traded scores again in the second, with Solomon's 18-yard reception in the end zone book ended by another Huskies' rouge and a 27-yard field goal by Cole Samson.
Heading into the third with a 14-12 lead, the Rams broke away with three unanswered touchdowns.
Solomon hauled in a 28-yard pass from Mueller before Kiapway added two quick touchdowns on the run to give Regina a 35-12 lead.
Saskatchewan attempted a comeback in the fourth.
Huskies quarterback Chase Bradshaw, who went 14 for 23 for 204 yards, two touchdowns and one interception, found Hillis on a 47-yard TD pass.
Hillis then caught his third TD of the game with 9:29 left in the fourth, but that's where Saskatchewan's charge ended.
No. 4 Rouge et Or 69, Redmen 0
At Montreal, Tristan Grenon and Alex Skinner each threw two touchdown passes for undefeated Laval (4-0) in a romp over McGill (1-3).Suggest a correction