A crowd of 14,209 fans attended the game at 40,000-seat Sam Boyd Stadium.
"Our defense stepped up to the plate big time," Las Vegas coach Jim Fassel said. "The things that we didn't do well at the end of the day we can coach. It was a good football game. It wasn't sloppy. It was hard hitting. It was what people want to see."
Losman, who spent the last five seasons with the Buffalo Bills, completed 21 of 31 passes for 226 yards. He threw a 1-yard TD pass to Dorsey with 13 seconds left in the second quarter, and had an 11-yard scoring pass to tight end Adam Bergen that gave Las Vegas a 17-14 lead with 11:07 left in the third quarter.
"I think guys are hungry, they're looking forward to next week," Losman said. "Ball security from the pocket standpoint was my biggest concern. These guys did an excellent job. The guys responded very well."
The Locomotives made it 30-17 on Dorsey's 9-yard TD run with 2:18 remaining in the game. Dorsey had nine carries for 63 yards and caught four passes for 19 yards.
"Dede is a flash-and-dash-take-it-to-the-house guy," Fassel said.
Graham Gano scored the first points in league history, hitting a 33-yard field goal with 3:20 left in the first quarter for the Locomotives.
The UFL's first touchdown came when Redwoods quarterback Shane Boyd scored on a 4-yard run with 11:03 left in the second quarter. California increased its lead to 14-3 on Cory Ross' 4-yard run with 8:45 remaining in the second quarter.
The Locomotives scored their first touchdown on Losman's scoring pass to Dorsey that cut it to 14-10. Following Losman's TD pass to Bergen, the Locomotives increased their lead to 20-14 on Gano's 39-yard field goal with 8:05 left in third quarter.
The Redwoods made it 20-17 on Parker Douglass' 26-yard field goal with 52 seconds remaining in the third quarter, but Las Vegas countered with Gano's 53-yard field goal with 5:32 left in the fourth quarter.
"I feel like our guys played well," California coach Dennis Green said. "I liked the way they played. I liked their effort. We didn't run the ball well in the second half. We were really chasing the rabbit into the rabbit hole in the second half."
The UFL follows mostly NFL rules. Visible differences from the NFL are that all of the referees wear solid red shirts and black pants and the yard-line and end-zone markers, as well as the sideline crew's vests, are lime green. There are also LED screens on one sideline and both end zones.
The four UFL teams will each play six games in the regular season. The championship games is set for Nov. 27 in Las Vegas.