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.
"Just playing harder and being more active," Solomon said. "I'm more focused. I'm trying to take every possession like it's my last possession. I just want to get better individually and collectively."
The Bears didn't have much problem against the smaller, slower Thunderbirds.
Southern Utah shot just 29.3 percent, committed 15 turnovers and was outscored 26-6 in the paint.
"They were flat-out better than we were," Thunderbirds coach Nick Robinson said. "(Cal) was more disciplined defensively, they did a great job on the boards and hit open shots that we weren't capable of hitting."
It was a good tune-up for the Bears, who fly to Hawaii to play Arkansas in the Maui Invitational next Monday.
The game matched Montgomery against one of his former players. 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.
He went back to bench not long after, falling three rebounds short of a third double-double in four games.
"He's hanging around the paint," Montgomery said. "I would be disappointed if he doesn't average double-figure rebounds, frankly. His mindset is he can get every board."
Wallace later made a 3-pointer and followed with a three-point play to push Cal's lead to 68-30.
The Thunderbirds couldn't keep up.
Justin Cobbs added six points and eight assists for the 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.
The Bears had just two players in double figures but led comfortably the entire way in the first-ever meeting between the two schools.
A.J. Hess scored 14 points for Southern Utah.
Cal 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.