Fifty of Green's 104 total passing yards on the day came during an 80-yard drive in the fourth quarter that led to a Johnson one-yard touchdown run to give Kansas City a 17-13 lead.
The Raiders had held the lead for 28 minutes leading up to the Chiefs final scoring drive.
Sebastian Janikowski capped two straight 11-play drives with field goals, connecting from 41 yards and 36 yards to make the score 7-6.
Aaron Brooks got the Raiders in the end zone on the next drive, giving them three straight series where they netted points. Brooks went 3-for-3 for 44 yards, tossing a strike to Courtney Anderson in the back of the end zone from two yards out to give Oakland their first lead, 13-7 at the half.
Lawrence Tynes added a 37-yard field goal in the third quarter, closing the gap to three points.
With a minute and a half on the clock, the Raiders had the final say. Ronald Curry made a tremendous 39-yard reception from Brooks to set the Raiders up at the eight-yard line with 30 seconds to go in the game and Oakland down by four. With several chances to hit the end zone and take the lead, Brooks dropped back to pass and tried to zip the ball into Randy Moss, but he was picked off by Jared Page to seal the Kansas City victory.
Oakland has lost seven straight games to the Kansas City Chiefs.