Gibbs and Miller, a pair of graduate transfers, each got off to a nice start in their first game with the Huskies. Gibbs, who also played at Texas and Seton Hall, also had four assists. Miller, who came over from Cornell, blocked three shots and had two steals.
''We just wanted to come in and be the best versions of us as possible and fit in where we could,'' Gibbs said.
UConn's 7-foot center Amida Brimah dominated underneath, finishing with 18 points, seven rebounds and nine blocked shots, one off the school record shared by Hasheem Thabeet (three times), Emeka Okafor and Donyell Marshall.
Till Gloger led Maine with 17 points.
Connecticut led the entire game in its 84th win in the 100 meetings of the two programs. The Huskies were up by 12 at the break and scored 34 of the next 38 points to put the game away.
Brimah had eight points and two blocks during an 11-0 run to open the second half.
''The only way you can have more energy is to have fun playing the game,'' he said.
The Huskies held Maine to 30 percent shooting while hitting 54.5 percent of their shots from the floor. They outscored Maine 54-22 in the paint and outrebounded the Black Bears 52-40.
Coach Kevin Ollie has been emphasizing a statistic he calls ''kills,'' stopping the other team on three consecutive possessions. UConn had nine of those, he said, six in the second half.
''Our switching defense really gave them trouble and then we started rebounding the basketball,'' Ollie said. ''Twenty assists, eight turnovers and 15 blocks is pretty good.''
Rodney Purvis chipped in 10 points and Calhoun had eight for UConn.
The Huskies played without senior forward Phil Nolan, who injured his right foot in the Huskies' final exhibition game.
UConn has won 59 of its last 71 openers.
UConn: The Huskies announced Friday the signing of a highly touted four-member recruiting class. The group includes guard Alterique Gilbert (Lithonia, Georgia), power forwards Mamadou Diarra (Queens, New York) and Juwan Durham (Tampa, Florida) and small forward Vance Jackson (Altadena, California). ''They don't overlap each other, which I like in my classes,'' coach Kevin Ollie said. ''I don't want two players just alike, because that's not fair to the players or the program.''
UConn is home again on Tuesday to play New Hampshire.