On the final play of the game, New England's Jakobi Meyers tried to recover a fumbled ball, but it was grabbed by Las Vegas' Chandler Jones and he returned it 48 yards for a touchdown.
The team decided to run a series of pitches in the last minute in order to avoid overtime. Stevenson threw the ball across the field and into the arms of Jones, who had an open field in front of him.
The Raiders were able to escape with a victory after allowing the Patriots to score 21 unanswered points. Las Vegas scored two touchdown in the last 32 seconds to ruin New England's playoffs hopes.
Stevenson, who went to high school in Las Vegas, had 19 carries for 172 yards, including a 34 yard touchdown in the fourth quarter that appeared to put the game away.
The Raiders came back in the last minute. The quarterback found Cole in the left corner of the end zone for a touchdown. Cole's left foot came down near the boundary, but the play was upheld on review.
The final play of the game will lead to questions about the strategy of the New England coach who lost to his former assistant.
The last three games of New England's schedule are against teams that are in the playoffs.
Carr threw for 231 yards and three touchdown. Josh Jacobs ran for 93 yards on 22 carries as the Raiders ended a six game losing streak to the New England.
The Raiders scored two touchdown in the last 5:18 of the first half to take a commanding lead.
He caught a 25-yard touchdown pass. It was his first game since the injury.
Malcolm Koonce blocked a punt with 23 seconds left and Carr completed a 5-yard touchdown pass to Mack Hollins.
The Raiders were in the third quarter. Kyle Dugger jumped out of the way of Davante Adams to return the pick for a touchdown.
Nick Folk kicked a 47-yard field goal with 1:21 left in the third quarter and a 54-yard field goal early in the fourth to give the Pats a chance to win.
The AP contributed to the story.