In a game that saw four fourth-quarter lead changes, both teams erupted for 935 total yards.
Nelson's touchdown catch capped a 14-play, 80-yard drive and gave Buffalo a three-point edge. Jason Campbell then gave the Raiders one last shot with a 24-yard pass to Denarius Moore, leaving just six seconds on the clock.
Following an incomplete pass, Campbell threw to the end zone from his own 44- yard line and Searcy came down with the ball in traffic for the game-sealing interception.
"Denarius did have his hand on the ball, but it looked like the defender had control of it and obviously they came away with that one," Raiders head coach Hue Jackson said.
The Bills (2-0) overcame a 21-3 halftime deficit by scoring touchdowns on each of their five second-half possessions.
This is the first time Buffalo has started 2-0 since they began 4-0 in 2008. They finished 7-9 that season. The Bills defeated Kansas City 41-7 in week one.
Ryan Fitzpatrick completed 28-of-46 passes for 264 yards and three scores while throwing one interception. Fred Jackson scored twice and totaled 117 yards on 15 carries. He added two catches for 23 yards.
"He made great decisions out there," Bills linebacker Nick Barnett said. "He's a good locker room guy, he keeps his composure, if he keeps doing that we may have a guy on our hands."
Nelson had 10 receptions -- including five on the final drive -- for 83 yards and the winning score. Stevie Johnson added 96 yards and a touchdown on eight catches.
Campbell threw from 323 yards and two touchdowns of 23-of-33 passing. His lone interception came on a Hail Mary to end the game.
Darren McFadden ran for 72 yards and a score on 20 carries, while catching seven balls for 71 yards and a touchdown for Oakland (1-1), which was coming off a Monday night win in Denver to open the season.
With Raider playmakers Jacoby Ford, Louis Murphy and Darrius Heyward-Bey out with injuries, Moore exploded for 146 yards on five catches, including an amazing 50-yard touchdown grab in double coverage.
Michael Bush capped off an impressive 14-play, 71-yard drive with a one-yard touchdown plunge to put the Raiders on the board early on in the second quarter.
Fitzpatrick threw an interception to Stanford Routt on the Bills' ensuing position to put the Raiders in prime field position at the Buffalo 34-yard line.
Oakland took advantage and went ahead 14-0 with a five-yard touchdown run by McFadden.
On 3rd-and-8 from the Oakland 14-yard line, Rolando McClain and Michael Huff tackled David Nelson just shy of the first- down marker to force the Bills to settle for a 25-yard Rian Lindell field goal to finally put the Bills on the scoreboard.
Oakland worked the two-minute drill to perfection as they scored their third touchdown in as many possessions when Campbell snuck in from a yard out to increase the lead to 21-3. The drive was highlighted by a Moore 42-yard reception down the right sideline, and a Michael Bush 22-yard run to put the ball on the one.
The Bills opened the third quarter with a three-play, 80-yard drive, concluded by a Jackson 43-yard touchdown run to cut the deficit to 21-10.
The Raiders followed with a nice drive of their own, converting three consecutive third downs, but McFadden put the ball on the ground and Buffalo recovered at their own 43-yard line.
Buffalo turned the turnover into six when Stevie Johnson finished off a seven- play, 57-yard drive with a seven-yard touchdown reception.
After an Oakland three and out, Buffalo took their first lead of the game on a Jackson one-yard touchdown run to make it 24-21 early in the fourth.
The see-saw went back in the Raiders favor on the ensuing possession with a McFadden 12-yard touchdown reception to regain the advantage, 28-24.
A huge defensive holding penalty by Oakland's Chris Johnson on a 3rd-and-goal gave the Bills a new set of downs. Two plays later, Fitzpatrick found Scott Chandler in the back of the end zone for a six-yard score to put the Bills back in front 31-28 with 4:48 to go. Johnson had two key catches on the drive including 17 and 12-yard receptions. C.J. Spiller added a 26-yard run.
The pendulum swung back in Oakland's favor as the rookie Moore came up with another big catch as he pulled down a 50-yard touchdown between two Bill defenders. Oakland led 35-31 with 3:41 to go.
Pandemonium broke out when Nelson hauled in the game-winner. He accounted for 37 yards on five catches on the drive.
Jason Campbell's Hail Mary attempt was intercepted by Da'Norris Searcy in the end zone to end the game.
Buffalo won 24-23 in their last meeting against Oakland on September 21, 2008. Lindell kicked a game-winning field goal as time expired...Stevie Johnson has 12 touchdown catches for Buffalo in his last 16 games...Sebastian Janikowski has yet to allow an opponent to return a kickoff.