Arizona (16-2, 4-1 Pac-12) came out shaky at both ends in the Pac-12's first game between top-10 teams in nearly seven years. The Wildcats rallied behind McConnell, the pass-first point guard who created his own shots while still setting up his teammates.
Johnson took over in the second half and the Wildcats shot 49% against one of the nation's toughest defensive teams to win their 32nd straight home game.
The Wildcats also outworked the Pac-12's best rebounding team, grabbing 21 more than the Utes (14-3, 4-1), including 17 on the offensive glass that led to 18 second-chance points.
McConnell had six assists, and Brandon Ashley added 14 points and eight rebounds.
Shaquielle McKissic scored 16 to lead five players in double figures for Arizona State (9-9, 1-4 Pac-12). Barnes scored 13, going four for six from three-point range.
Askia Booker, coming off a career-high 30-point game in the Buffaloes' loss at No. 10 Arizona on Thursday, led Colorado (9-8, 2-3) with 21. Jaron Hopkins added 20.
Gary Payton II added 13 points and 13 rebounds for Oregon State (12-5, 3-2 Pac-12).
DaVonte Lacy, playing on a sore right knee that limited him to 10 minutes in the first half, scored all of his team-high 16 points in the second half for Washington State (9-8, 3-2). Josh Hawkinson had 11 points and nine rebounds for the Cougars.
Anthony Brown added 18 points and Stefan Nastic had 13 points to go with 12 rebounds for Stanford (13-4), which won its third straight and seven of eight overall.
Rodney Purvis scored 14 points to lead Connecticut (9-7), which lost its second straight after winning five of their previous six. Omar Calhoun added 11 points.