The Wildcats, seeded sixth in the West Region, coasted to a comfortable decision that set up a third-round meeting with Harvard, which pulled off a shocking 68-62 win over New Mexico for its first NCAA Tournament victory.
Arizona shot 56 percent from the field, hit 9-of-17 from 3-point range and claimed 27 more rebounds than did the Bruins.
Lyons scored 23 points while Kevin Parrom, Kaleb Tarczewski and Nick Johnson all had 12 for the Wildcats (26-7).
Arizona's win helped the Pacific-12 Conference to finish the first full day of the NCAA Tournament with a 3-0 record. Oregon and California also posted victories for that league.
The Wildcats went on a 9-1 run to finish the first half, taking a 32-20 lead at intermission.
Belmont (26-7) was led by Kerron Johnson with 22 points. The Bruins, who won the Ohio Valley Conference tournament title in their first year in the league, is winless in six NCAA appearances.