The teams last met in 2004, with UConn winning 2-1.
Quinnipiac won the MAAC championship Sunday by defeating Monmouth in penalty kicks after a scoreless tie through regulation and overtime.
The tournament victory is the first in Quinnipiac's Division I history, which began in 1999-00. The Bobcats are 9-4-7 and would match the program single-season record with another victory.
No. 11 UConn also played to a scoreless tie Sunday but lost the American Athletic Conference championship game in penalty kicks to South Florida. The Huskies (11-2-6) have a 13-game unbeaten streak and have not allowed a goal in 585 minutes.
The UConn-Hartford winner will advance to play No. 16 overall seed Maryland-Baltimore County.
UMBC defeated Hartford 4-0 in the America East championship game. The Hawks (13-4-4) had hopes for an at-large bid but did not make the 48-team field. Hartford posted its most victories since winning 17 in 1996.