Chattanooga (5-10, 1-2 Southern Conference) shot 52.1 percent (25 of 48), while Furman was 16-for-56 form the field, including 6 of 38 in the second half.
With Doaks' first two points he passed Eric Smith (1978-81) for eighth place on the Mocs' all-time scoring list.
Chattanooga scored 25 points off of 18 Paladins (2-11, 0-3) turnovers.
Doaks added nine rebounds, as the Mocs won the battle of the boards at 32-26.
McDowell was 6-for-13 from 3-point range for the Mocs who shot 36.4 percent from beyond the arc (8 of 22).