Nelson's reception came at the end of a 14-play, 80-yard drive and Da'Norris Searcy sealed the victory by picking off Oakland's last-chance Hail Mary pass in the end zone in a game with four fourth-quarter lead changes.
Buffalo (2-0) trailed 21-3 at halftime but responded by scoring touchdowns on each of its five second-half possessions, with Ryan Fitzpatrick going 28-of-46 through the air for 264 yards and three scores.
Fred Jackson logged a pair of TDs and totaled 117 rushing and receiving yards.
Oakland's Jason Campbell amassed 323 passing yards and two touchdowns, completing 23-of-33 attempts. His lone interception came on the last play of the game.
Darren McFadden ran for 72 yards and a score on 20 carries, while catching seven balls for 71 yards and a touchdown. Denarius Moore racked up 146 yards on five catches for the Raiders (1-1).