Oakland drew up a reverse play, with Woodson taking the handoff and seemingly looking to throw what would have been the winning touchdown to quarterback Derek Carr. Instead, he was chased out of bounds.
The Raiders did, however, take the lead for good on Sebastian Janikowski's 31-yard field goal that concluded the drive.
A source told ESPN's Mark Schwarz earlier Thursday that Woodson, a safety, would very likely play offense in some situations. He was expected to play wide receiver and possibly return a few punts, though with the game being close throughout he didn't get his chance on offense until OT.
Woodson got a loud ovation as he was introduced last with the defensive starters and was the only Oakland captain for the pregame coin toss.
"This is my last game in the Coliseum, but just know I'll never leave you," Woodson told the crowd after the win. "Go Raiders!"
On Tuesday, Oakland offensive coordinator Bill Musgrave said Woodson, who won the Heisman Trophy at Michigan for his defensive, offensive and special-teams prowess, could line up at receiver for a play or two.
"We may have something up our sleeve," Musgrave said. "It might be the right time to do it."
Woodson, 39, announced on Monday that he will retire at the end of the regular season. An 18-year NFL veteran, he had been planning to announce his retirement in January but decided to make his intentions known this week in order to say goodbye to the Oakland fans.
He was named to his ninth Pro Bowl on Tuesday.
Information from The Associated Press was used in this report.