Fans stormed the court after the Irish's rousing victory. It was the eighth time Notre Dame has beaten a No. 1 team -- that ties for fourth-most all-time, with North Carolina having the most with 12.
The Orange (20-1, 7-1) played without starting center Fab Melo, who did not make the trip and will not play Monday against Cincinnati.
Without Melo in the middle, the 6-foot-9, 248-pound Cooley was a major force for Notre Dame (12-8, 4-3) and the Irish won the rebound battle 38-25.
Melo had started all 20 of the Orange's first games, was their leading rebounder with 5.7 a game, averaged 7.2 points and three blocks. School officials gave no explanation why the talented center did not make the trip. C.J. Fair started for the Orange.
James Southerland scored 15 points for Syracuse, which shot just 34 percent and had its lowest scoring game of the season. Scott Martin added 13 for Notre Dame, which hit 50 percent of its field-goal attempts.
Southerland's 3-pointer with 53.9 seconds left brought the Orange to within 62-56 before the Irish held on as Jerian Grant sank four free throws in the final 32 seconds.
It was the first time the Irish have beaten a top-ranked team since 1987 when they defeated North Carolina, also in South Bend. One of the Irish's most dramatic victories over a No. 1 came in 1974, when they stopped UCLA's 88-game winning streak by 71-70.
Syracuse coach Jim Boeheim was denied his 877th career victory, which would have put him in sole possession of fourth place among Division I men's coaches.
Notre Dame led in the first half by as many as 18 and was up 35-23 at the half, shooting 54.4 percent and holding the Orange to 2.6 (8-for-18). Syracuse was only 4-of-13 from the 3-point line and was beaten on the boards 20-13 as Notre Dame seemed to be half step quicker.
Syracuse got off to a better second-half start and whittled the lead to eight less than three minutes in. But Martin hit another 3-pointer for the Irish as the shot clock was winding down and Cooley -- benefiting from Melo's absence -- bulled his way in for a layup to restore the lead to 12. Cooley then dropped in two free throws and Martin again sank a 3-pointer and the Irish were rolling with a 17-point lead.
The Orange then went on a 9-2 run and Kris Joseph's 3-pointer made it a 10-point game with 7:43 to go. Syracuse again cut it to eight before Cooley roared down the court for a dunk with just over five minutes left.
Triche's three-point play with 2:24 left cut it to seven as the Orange made a final run.
Pat Connaughton, inserted into the Irish starting lineup, had a pair of 3s in the early going and Notre Dame bolted to an 11-2 lead.
Notre Dame kept up the long-range accuracy, making four of its first six attempts. And when Eric Atkins grabbed a rebound and went the length of the floor for a layup, the Irish were up 21-10 as the fans at Purcell Pavilion went wild.
And without Melo in the middle, the Irish were all over the boards with an early 13-4 advantage.
Atkins picked up his third foul with 9:04 left, but Jerian Grant's 3-pointer gave the Irish a two-touchdown lead at 28-14.
The Orange missed 14 of their first 19 field-goal attempts and nothing was falling. Tom Knight's left-handed shot in the lane doubled the score, putting the Irish up 32-16.
Alex Dragicevich's 3-pointer as the shot clock was running down put the Irish up 35-18 with 1:12 left in the half. Dion Waiters then responded with a pair of quick 3-pointers to get the Orange to within 12 at the end of a frustrating first half.
The 23 points represented the Orange's lowest-scoring half of the season.