Justin Cobbs added six points and eight assists for the Golden Bears (4-0), who overcame an off night by leading scorer Jabari Bird. Cal's freshman guard had eight points but shot just 1 of 3 and committed eight turnovers.
Solomon finished with a season-high 14 points, seven rebounds and three blocked shots while Wallace had 15 points and four rebounds. The two combined with David Kravish to score 15 points during a 24-3 run in the second half when Cal pushed its lead to 38.
A.J. Hess scored 14 points for Southern Utah. The Thunderbirds (1-2) shot just 29.3 percent.
The Bears had just two players in double figures but led comfortably the entire way in the first-ever meeting between the two schools.
The game matched Cal coach Mike Montgomery against one of his former players. Southern Utah coach Nick Robinson, in his second year with the Thunderbirds, spent three seasons at Stanford when Montgomery coached the Cardinal before making the jump to the NBA.
Montgomery returned to the college ranks in 2008 and has turned Cal from an also-ran to a perennial contender in the Pac-12. The win over Southern Utah raised the Bears record to 37-6 at home against non-conference opponents during Montgomery's tenure.
This time, the teacher got the upper hand with a little help from Solomon, who helped the Bears dominate in the low post.
Solomon got the Bears going early then provided another boost when he scored eight of Cal's first 14 points coming out of halftime.
Wallace later made a 3-pointer and followed with a three-point play to push Cal's lead to 68-30.
The Thunderbirds, who were coming off 33-point loss at Utah State, couldn't keep up. They committed 15 turnovers and were outscored 26-6 in the paint.
Cal took an early lead and never looked back.
The Bears scored the first 14 points of the game and were up 33-10 following consecutive 3s from Cobbs and Wallace with 4:48 left in the first half.
Trey Kennedy and Hess made back-to-back 3-pointers for Southern Utah and Hess added a free throw to cut the gap to 39-20 at the break.
The Thunderbirds, who had just five points through the first 10 minutes, shot 22.2 percent from the floor in the first half.