Mosqueda-Lewis finished with 22 points, all in the first half. Morgan Tuck had 18, and Moriah Jefferson added 16 for the Huskies (30-4), who advanced to the second round for the 20th straight time in their 25th consecutive tournament appearance.
The Huskies will play eighth-seeded Vanderbilt on Monday. The Commodores beat Saint Joseph's 60-54 earlier Saturday.
Stacey Barr had 14 points for Idaho (17-16), which was playing its second NCAA tournament game ever after upsetting Seattle for the Western Athletic Conference title.
UConn led by as many as 74 in the second half before Idaho made some baskets late.
Connecticut put this one away early, opening the game with a 22-3 run and holding Idaho without a basket for more than 5 minutes.
The Huskies led 58-17 at the break, and it didn't get didn't get better for the Vandals after halftime. UConn stretched the lead to 69-17 on a 3-pointer by Kelly Faris. Kiah Stokes' jumper with more than 12 minutes to go, made it 78-18. The Vandals scored their first point of the second half on a free throw with 12:31 left.
A basket by little used Heather Buck pushed the lead past 70 at 93-22.
UConn had first-round wins of 71 points over Hampton in 2000 and 72 against Long Island in 2001.
The Huskies beat Kansas State 72-26 in last year's tournament, the record for fewest points in a game.
Connecticut shot 61 percent from the floor, while holding Idaho to 14 baskets on 53 attempts (26 percent).
UConn outrebounded Idaho 45-23, and outscored the Vandals in the paint 46-8.
UConn played the game without one of its key post players. Freshman Breanna Stewart injured her left calf in practice on Friday, and sat out as a precaution. She is expected to be ready to play on Monday.
The Huskies are trying for a record sixth consecutive trip to the Final Four and an eighth national championship. They have won 30 games for an NCAA record eighth straight season.
The 30th win came on coach Geno Auriemma's 59th birthday. The Huskies are 8-1 when playing on that day..
This was the first meeting between these programs, but the teams weren't entirely unfamiliar to each other. Mosqueda-Lewis and Idaho's Connie Ballestero went to elementary school together in Southern California, and they played youth basketball with Idaho's Krissy Karr.
UConn is a top seed for the seventh straight year. The Huskies are 21-2 in first-round games, which doesn't include the two seasons they received first-round byes.
They came in having won their last six first-round games by an average of 41 points.
The win was the 86th for the Huskies in the NCAA tournament, second only to Tennessee's 112.
Idaho had won five of six coming in.
The Vandals lost nine of their first 20 games this season, but finished strong, winning 14 of their final 20, and sweeping through the Western Athletic Conference tournament. Idaho also lost in the first round in 1985, 74-51 to Cheryl Miller and Southern California.