Lyles made 10 of 14 shots, had seven rebounds, four steals and three assists. Elliott went 13 of 14 from the foul line and dished eight assists.
Troy Reid-Knight hit four 3s and had 18 points for the Black Bears (4-11, 0-2).
UMBC was up two at the half but used an 11-3 run to make it 58-50 with 12:02 to play. Reid-Knight pulled the Black Bears back into a tie with a 3-pointer at 9:33 but the Retrievers responded with a 16-3 run started by Lyles' five points.
UMBC shot 59 percent from the field and made 24 of 29 from the foul line while Maine was 4 of 8 from the line.