Millsaps (5-2) scored on a penalty kick with 32 seconds left in overtime.
"Losing in overtime is always tough to take, especially on the road against a well organized team," Huntingdon head coach Matt Williams said. "Our boys put in a great effort and we had our chances to get a result out of the game, it just wasn't to be. We'll build off of this performance and come back better next week."
The Hawks (1-3-2) held Millsaps scoreless through the first half before the Majors scored in the 53rd minute. Wier tied the game in the 60th minute.
With Millsaps taking 31 shots for the game, including 18 shots on goal, Brown tied Huntingdon's NCAA-era single-game record for saves with 16. He recorded six saves in the first half, nine in the second half and one in overtime.
Huntingdon hosts Sewanee on Friday at 7 p.m. at Samford Stadium.