"Both teams were worthy of winning this game," Krzyzewski said. "Both teams were worthy of winning up there (at Syracuse). Going 1-1 is probably how it should be."
The lead went back and forth for the first 10 minutes of the second half before Duke grabbed a 51-45 advantage with less than eight minutes to play.
Even though the Blue Devils were in their fourth game in eight nights, they didn't wilt.
"We were able to keep on going," Parker said.
Krzyzewski said, "It's tough for people to understand when you play four games in eight days, especially with two on the road at 9 o'clock."
Parker's putback dunk with 4:25 left helped the Blue Devils to a 55-49 edge.
The Orange were within 57-56 on two free throws by guard Trevor Cooney with two minutes remaining.
Parker bulled in for a basket at the other end. He rebounded Cooney's miss, but then Parker failed to convert on the front end of a 1-and-1.
The score was tied 26-26 at halftime, although Duke never led in the opening 20 minutes.
But Duke pulled even with 1:06 left when Sulaimon scored off an Orange turnover.
Syracuse was fortunate that it grabbed 13 offensive rebounds in the first half because it was shooting only 28.6 percent (10-of-35) from the field at the break.
NOTES: Syracuse defeated Duke 91-89 in overtime three weeks earlier in a game that some consider the best college game of the season. ... This was Duke's first game against a No. 1 team since facing North Carolina on March 8, 2008. ... Syracuse and Duke both failed to protect double-figure, second-half leads in their previous games, with Syracuse falling to Boston College and Duke losing at North Carolina. ... This game began a season-ending stretch of four road games in five outings for Syracuse, which plays Monday night at Maryland. ... Duke is at home on Tuesday night against Virginia Tech, playing its fifth game in 11 nights.