Pryor threw two touchdown passes in the first quarter and Woodson tied an NFL record with his 13th defensive touchdown as the Raiders beat the San Diego Chargers 27-17 on Sunday night.
Pryor got the Raiders (2-3) off to a fast start in the latest West Coast game in NFL history with a 44-yard touchdown pass to Rod Streater on Oakland's first play from scrimmage.
"I thought he started the game out about as good as you can start out," coach Dennis Allen said.
Philip Rivers had his third 400-yard passing game of the season, throwing for 411 yards and two touchdowns. But he also had three interceptions as the Chargers played without injured starting offensive linemen King Dunlap and Chad Rinehart.
They also lost running back Ryan Mathews to a concussion in the first half.
"We came out and we were outplayed in all three phases," coach Mike McCoy said. "It's tough to go on the road and turn the ball over the way we did and win a football game on the road against a good football team. Too many big plays."
The game was shifted to a late-night start to allow time to convert the Coliseum to its football configuration after the Oakland Athletics played a baseball playoff game here Saturday night. The process took about 18 hours and was completed around 3:30 p.m., more than five hours before kickoff at 8:35 p.m.
The wait was more than worth it for Oakland fans who had plenty to cheer about right from the start as Pryor and the Raiders broke out to a 17-0 halftime lead.
The Chargers' first score didn't come easily as Nick Novak had a 37-yard field goal attempt blocked by Tracy Porter. But Ladarius Green picked up the ball behind the line of scrimmage and ran for a first down. Rivers appeared to throw a touchdown pass to Keenan Allen two plays later but the call was reversed after replay showed Allen got only one foot down inbounds.
That led to a second field goal attempt for Novak and he connected this time from 35 yards to cut Oakland's lead to 17-3.
The Raiders appeared to break the game open when Woodson scooped up Woodhead's fumble and ran it in to make it 24-3. That tied him with Darren Sharper and Rod Woodson for the most defensive touchdowns in NFL history.
"He's made a habit out of doing that his whole career. A defensive score, an interception to seal the game," Allen said. "That's what we expect out of him. He's been a playmaker for us and he'll continue to be a playmaker for us."
But Rivers and the Chargers didn't quit, scoring touchdowns on their next two drives on passes to Woodhead and Allen in the opening 5 minutes of the fourth quarter to cut the deficit to 24-17.
"He got hot and we had to keep punching back," Pryor said.
Pryor came up with one more big play, scrambling before hitting Brice Butler on a 20-yard pass on third-and-14. That set up Janikowski's 50-yard field goal that made it 27-17.
Pryor finished 18 of 23 for 223 yards and has committed no turnovers since throwing two interceptions in the opener.
"A lot of times you look up and something bad is about to happen and here he goes getting out of the pocket and he creates," Allen said. "It gives our team a sense of confidence."
Oakland rookie D.J. Hayden and Woodson added late interceptions to seal the win.
One week after Raiders fans spent much of the game booing Matt Flynn when he started while Pryor recovered from a concussion, there were only cheers for the quarterback this time.
The love fest for Pryor started immediately after Rivers threw an interception to Usama Young on the third play from scrimmage. The Raiders took a deep shot on the next play and Pryor connected on a perfectly placed 44-yard touchdown pass to Streater.
Pryor followed that deep shot with a methodical, 88-yard drive on Oakland's second possession, completing all seven passes for 61 yards capped by a 2-yard TD pass to Denarius Moore that gave Oakland a 14-0 lead after the first quarter for the second straight week.
Kevin Burnett then stuffed Woodhead on a fourth-and-goal carry from the 1 and Chimdi Chekwa recovered a fumbled punt to Eddie Royal to set up Janikowski's 47-yard field goal that made it 17-0 -- Oakland's biggest halftime lead at home since the AFC championship season in 2002.
NOTES: Rivers had three career 400-yard passing games before doing it three times in the past four weeks. ... Raiders RB Rashad Jennings left in the first half with a hamstring injury.