Grayson Allen added 15 points and Wendell Carter Jr. and Gary Trent Jr. each scored 14 points for Duke, which is part of the Elite Eight for the first time since winning the 2015 national championship.
Duke (29-7) takes on top-seeded Kansas, an 80-76 winner against fifth-seeded Clemson, on Sunday in the Midwest Region final.
Tyus Battle posted 19 points, Oshae Brissett provided 13 of his 15 points in the second half, and Marek Dolezaj had 13 points for Syracuse (23-14). The Orange won three close games to reach this stage of the tournament.
Bagley's tip-in gave Duke a 60-53 lead, but the Orange got within 63-60 before Trent's runner with 51.7 seconds to play. Howard countered with a pair of free throws.
Syracuse regained possession after Allen missed a free throw, but Duke fouled with seven seconds left before the Orange could launch a potential tying 3-point attempt.
Duke shot 2 of 17 from beyond the arc in second half, 5 of 26 from long distance overall.
Syracuse scored the first four points of the second half to cut its deficit to 34-31, resulting in Duke coach Mike Krzyzewski angrily calling a timeout and shedding his sports jacket.
Twice in the first five minutes of the second half, Syracuse missed free throws that would have resulted in three-point plays and a tie score.
Back-to-back 3-pointers by Trent and Allen, sandwiched around a 10-second violation on Syracuse, sent Duke to a 48-39 edge.
The Orange closed within 50-45 with 10:45 left, but center Paschal Chukwu picked up his fourth foul with more than nine minutes left.
Duke used a 10-0 run to end the first half with a 34-27 lead.
Duke went up 28-27 on two Allen free throws with 3:45 left. Those came following a Brissett missed dunk after the Orange corralled an offensive rebound, resulting in a Duke transition opportunity.
The Blue Devils outscored Syracuse 11-2 on free throws in the first half.
Syracuse led for almost 11 minutes, but the Orange didn't score in the final five-plus minutes of the half. Syracuse was charged with 12 turnovers in the opening half, 16 for the game.
Frank Howard and Brissett, who are two of Syracuse's three main scorers, combined to shoot 1-for-12 from the field in the first half. Howard wound up with six points.
The teams combined for three 3-point baskets in the first eight minutes, and each team had three treys by halftime.
The Atlantic Coast Conference teams met Feb. 24 in the regular season, with Duke posting a 60-44 home victory when both teams were held to season-low point totals.
--Field Level Media
Syracuse | Duke | |
Tyus Battle 19 | Scoring | Marvin Bagley III 22 |
Tyus Battle 5 | Assists | Grayson Allen 8 |
Frank Howard 8 | Rebounds | Wendell Carter Jr. 12 |
Oshae Brissett 5 | Free Throws Made | Wendell Carter Jr. 8 |
Oshae Brissett 2 | Steals | Grayson Allen 2 |
Oshae Brissett 1 | Blocks | Marques Bolden 1 |