Toliver, who earlier this year became the program's all-time assists leader, passed 1,500 points for her career, the 10th player in Maryland history to do so.
Marissa Coleman added 22 points, passing 1,600 points for her career and moving into sixth-place all-time.
Doreena Campbell, who grew up 45 minutes from the Maryland campus, led UCLA with 25 points, scoring 14 in the first half.
UCLA (2-1) never recovered from a rough start, that saw them trail 30-10 in the first half and shoot just 18.2 percent from the floor. Maryland led 41-22 at the break and its lead never dropped out of double-digits in the second half.
It was the second season in a row that Maryland had beaten in the Bruins.