"I always wanted to play here because all the great players had a chance to play here," the 6-foot-4 senior said. "This was a chance for us to show everyone that Temple is a real program."
Anthony Lee had a career-high 21 points for the Owls (9-2), who were coming off a 10-point home loss to Canisius.
This is the fifth straight season Temple has beaten a top 10 team while being unranked.
The latest win in that stretch game with the combination of Wyatt from the outside and Lee inside.
"We wanted to go inside and out and that meant me going up strong and fighting for rebounds," said Lee, who had nine rebounds, five offensive, and worked the baseline again and again against Syracuse's vaunted zone. "That's playing the Temple game."
Dunphy said Wyatt challenged himself after a poor game against Canisius.
"He made some really good plays when we were struggling to score and had to stay in the game," Dunphy said.
It was the first non-conference regular season loss since 2008, ending a streak of 52 such wins in a row.
The Orange led by two at halftime but never took a lead in the second half even though there were four ties, the last at 59-59 with 10:23 to play.
C.J. Fair had a career-high 25 points for Syracuse (10-1), which had its 52-game regular-season nonconference winning streak snapped. Jim Boeheim remained at 900 wins, two behind Bob Knight for second place all-time among Division I men's coaches. Duke's Mike Krzyzewski has 938 wins.
Wyatt made all 15 of his free throw attempts and Lee was 11 of 14 as the Owls were 29 of 36 overall.
Syracuse was 19 of 34 from the line including missing four in the final 6 minutes when it was mostly a one-possession game and point guard Michael Carter-Williams finished 7 of 15.
"They made free throws, we didn't," Boeheim said. "You don't like to say it comes down to that, but when you miss 15 free throws it's tough to win any game."
Carter-Williams took the heat.
"If I make free throws we win the game," he said.
Temple hit three 3-pointers in an 11-3 run that gave it the lead for good. Scootie Randall started the run with a 3 that broke the 59-all tie. He closed the run with another 3, his only points of the game.
The 3-point line also hurt the Orange, who were 2 of 12 from behind the arc while Temple was 8 of 24.
"It was one of those nights when it wouldn't fall," said Fair, whose only 3-point attempt of the game brought the Orange within 74-72 with 3:01 left but the Owls went 11 of 15 from the free throw line over the final 2:30.
Temple's last field goal was an offensive rebound by Quenton DeCosey with 5:41 left that gave the Owls a 72-66 lead.
Rahlir Hollis-Jefferson had four points and 10 rebounds for the Owls.
Brandon Triche had 17 points for Syracuse. Baye Moussa Keita added 12 and Carter-Williams, who leads the nation in assists at 10.7 per game, had 13 points and six assists.
"Wyatt was able to create a lot of contact and that got him to the free throw line," Carter-Williams said. "They didn't play off me and I have to get used to that. We have to learn from this. It's a long season."
Temple missed 10 of its first 12 shots in falling behind 19-10. The Owls, behind Wyatt who had 20 points in the first half, started hitting shots against the Orange's zone defense and they made nine of their next 14 shots and tied the game at 35. Syracuse scored five straight points but Wyatt capped his big half with a 3-pointer with 17 seconds left and Temple was within 40-38 at halftime.