Laird scored on a 1-yard plunge early in the fourth quarter to put the Bears ahead 27-20 and then broke off a 73-yard touchdown run to seal the win and help California (2-0) survive the Wildcats' upset bid.
Laird, a junior, finished with 191 yards and three touchdowns on just 12 carries.
Weber State quarterback Stefan Cantwell completed 25 of 44 passes for 431 yards and a touchdown.
Trailing by 10 points late in the second quarter, Cantwell threw a 55-yard touchdown pass to big-play receiver Rashid Shaheed, and Trey Tuttle kicked a 45-yard field goal in the final seconds of the first half to send the Wildcats into halftime with a 20-17 lead.
Weber State (1-1) outgained California 327-208 in the first half.
Cal tied the game at 20 on Matt Anderson's 40-yard field goal to open the fourth quarter.
Laird had a 51-yard touchdown run and wide receiver Demetris Robertson had a 34-yard touchdown run in the first half for the Bears.
Saturday's game against Weber State of the FCS was sandwiched in between a pair of big non-conference games for Cal. The Bears were coming off a big road win at North Carolina last week and host Ole Miss next week.
Shaheed finished with four catches and 149 yards.
Cal quarterback Ross Bowers completed 20 of 28 passes for 200 yards.
The Bears surrendered 571 yards to Weber State but still found a way to win. Cal's defense came up with a fourth-down stop late in the fourth quarter when Weber State was driving for a potential tying touchdown.
Laird squirted free on the Bears' next possession, racing 73 yards to help Cal prevail.