Joyce shot 10 of 16 from the floor. Wayne Sparrow had 15 points and eight rebounds, and Jourdan Grant chipped in 11 points and dished out five assists with three steals for the Retrievers, who shot 26 of 48 from the field for 54.2 percent.
UMBC (2-9) has won back-to-back games since opening its season with nine-straight losses.
Joyce scored to break a 38-all tie and spark a 13-5 run to make it 51-43 with 11:31 left. Kennesaw State pulled within 58-51 with 3:32 remaining, but the Retrievers closed on an 8-2 surge to seal it.