Sebastian Janikowski booted three field goals -- including an NFL record-tying 63-yarder as time expired in the first half -- and Darren McFadden piled up 150 yards on 22 carries for the Raiders (1-0).
Campbell's one-yard TD run with 12:33 left in the fourth quarter was set up by McFadden's 47-yard gain on the previous play and gave Oakland a 23-13 lead.
Campbell finished 13-of-22 passing for 105 yards and a three-yard TD toss to Marcel Reece.
Kyle Orton completed 24-of-46 passes for 304 yards, a score and a pick off for the Broncos (0-1).
Denver's Brandon Lloyd made six grabs for 89 yards.