Cincinnati, Villanova and Notre Dame also won second-round games Wednesday.
Syracuse had lost four of its last five regular-season contests, but Southerland helped the Orange (24-8) set up a quarterfinal meeting with fourth-seeded Pittsburgh.
C.J. Fair scored 14 of his 16 points in the second half while Brandon Triche added 17 points for Syracuse. Aaron Cosby led Seton Hall (15-18) with 22 points.
Cincinnati reached the quarterfinals with a 61-44 decision over Providence, Villanova defeated St. John's 66-53 and Notre Dame was a 69-61 winner over Rutgers.
Cincinnati will take on Georgetown in the quarterfinal opener Thursday with Villanova meeting Louisville and Notre Dame facing Marquette.
Pat Connaughton led Notre Dame (24-8) by making 6-of-8 from 3-point range. The Fighting Irish are trying to get to the conference championship game in their last appearance in the event.
Mouphtaou Yarou went 9-of-10 from the field and had 18 points in Villanova's win. The Wildcats (20-12) appear to be a lock for the NCAA Tournament after a big win over Georgetown last week and Wednesday's decision only helped matters.
Cincinnati's effort against Providence was led by Sean Kilpatrick's 17 points. Cincinnati (22-10) held the Friars to just 28 percent shooting and Providence scored only one field goal in the game's first 6:30.