Two minutes into overtime, Keefer won a 50-50 ball at the top of the 18-yard box and slipped her shot past Diplomats keeper Gabby Panayotakis for the game-winner.
Keefer's goal, one of two she had on the night, capped an evening in which the two teams traded goals all night.
Reanna Leoni, who had two goals and one assist for the Dips, scored the first of her two goals by hitting a 35-yard rocket past Hornets starting keeper Charlotte Evans in the 28th minute.
The back-and-forth continued as Spaziani scored off a Keefer assist in the 42nd minute before F&M answered in the 56th.
Keefer's first goal, in the 78th minute off an Izzy Piazza assist, gave SU its third lead of the night. The Dips again answered, with Leoni scoring unassisted to force OT.
Keefer then played the hero by notching the golden goal 2:19 into the first 10-minute extra session.
"Not the prettiest game, but we got the result," SU coach Liz Pike said. "It was great to see our freshman score a couple of goals tonight, but we have some things to work on."
Shenandoah outshot its visitors 11-6 and took the game's only two corners.
SU takes to the road this weekend for a pair of games in the Garden State. The Hornets play at Rutgers-Camden Saturday and Stockton on Sunday.
Note: With the win, all four fall teams that use Sprint Field at Shentel Stadium (field hockey, football, men's soccer and women's soccer) were victorious in their first games on the new FieldTurf surface.