The Orange were led by junior Randy Staats who notched a career-high 9 points after scoring 5 goals and dishing out 4 assists.
SU used an 8-1 run in the second half to finish off Big Red.
The rivalry dates back to 1920, with the two schools having met every season since 1979.
Prior to Tuesday's game, six of the previous 10 meetings between the two schools had been decided by a single goal.
With the loss, the Big Red fell to 9-2 on the season, while the Orange improved to 7-3.
SU will next play the University of North Carolina at the Carrier Dome on Saturday, April 12, in a critical ACC contest.
The Orange needs a win to keep its ACC Tournament hopes alive. Opening faceoff is scheduled for 6 p.m. and the game can be watched on ESPNU.
The Big Red heads to Hempstead for a non-conference game against No. 16 Hofstra on Saturday, April 12 at 1 p.m.