The Wildcats trailed 11-10 after the first quarter but rallied to outperform the Bears 13-8 and lead 23-19 at halftime.
Galena stormed out of the locker room and outscored Verona 24-12 to lead 43-35 heading into the fourth.
Tyler Aschwege recorded 32 points for Galena. Wyatt Stephens chipped in 16.
Scoring for Verona were: Nick Washam, 20; Wesley Kissinger, 16; Cody Ernsberger, 12; and Seth Losack, 3.
Verona hosts Purdy on Tuesday night. Tipoff is set for 6 p.m.