Montana scored only 15 points in the first half, barely reached that total in the second period and finished with just 11 field goals while shooting 20 percent.
The outmanned Grizzlies (25-7) had won both the regular-season championship and the tournament crown in the Big Sky Conference, but were no match for a team that played with a purpose.
For the second straight year going into the tournament, the Syracuse basketball program has been the subject of reports that it is the subject of an NCAA investigation. Nothing came of those reports a year ago.
With those stories as a motivation, Syracuse delivered the most one-sided victory to date in the tournament and set up a third-round meeting on Saturday with California -- a 64-61 upset winner over UCLA earlier in the evening.
Triche made 5-of-6 from the field and 8-of-10 from the foul line. C.J. Fair added 13 points for Syracuse (27-9), which with its win gave the Big East Conference a 3-1 record on the tournament's first full day.
No Montana player could score more than five points. The Grizzlies turned the ball over 21 times and were outrebounded by 11.