Dolson made 11 of her 13 shots from the floor for the Huskies (11-1), while Hayes connected on 8-of-11. As a team UConn made 59 percent of its shots.
Desiree Pina scored 12 points to lead the Stags (7-4), who had won four straight games prior to Thursday.
Brianna Banks and Kaleena Mosqueda-Lewis added 12 points each for the victors.
Dolson, a sophomore center dominated play right from the start, scoring 14 of the Huskies' first 16 points.
The Huskies have won eight straight games against their in-state rivals, though this was the first meeting between the schools since the 2001-02 season.
During a halftime ceremony UConn's 2002 national championship team were inducted as Huskies of Honor. Among those in attendance for the festivities Thursday were Sue Bird, Maria Conlon and Svetlana Abrosimova.