Minto tormented the Jets all evening, with his precision kicking in general play almost single-handedly booting the Jets out of the Intrust Super Cup premiership race.
Three of the Cutters four tries came directly from attacking kicks from the former Central Queensland playmaker.
Minto also produced a stunning second-half 40-20 that put the Cutters deep on the attack. The Cutters immediately came up with points with a slashing try from Liam Taylor extending their lead to 24-10.
It was a remarkable scoreline so early in the second half given that the two sides had gone into the half-time break locked at 10-10.
The Jets made the early running in the first half, with tries from Keiron Lander and Jarrod McInally putting the visitors in front 10-4.
But errors slowly started to creep into the Jets game and the Cutters were good enough to capitalise, with a Minto grubber producing a try in the right corner for Bureta Faraimo.
Faraimo notched an early second-half double when he chased through another superbly weighted kick from Minto.
The Cutters produced an enthusiastic chase for every kick, a facet of their game that impressed coach Kim Williams.
Their desperation in defence in the final 20 minutes also pleased Williams, whose team endured a few anxious moments in a tense finish.
The Jets closed the gap to eight points when Troy OSullivan was the first to a Dane Phillips grubber kick.
A brilliant passing movement saw Ipswich fullback Javarn White cross the line with eight minutes to play, but he was ruled to have lost the ball over the line.
The near miss virtually killed off Ipswichs brave comeback bid, as the Cutters went on to seal the win with a penalty goal and field goal.
MACKAY CUTTERS 27 (Bureta Faraimo 2, Liam Taylor, Kalifa FaiFai Loa tries; Liam Taylor 3, Matt Minto 2 goals; Matt Minto field goal) def IPSWICH JETS 16