The Panthers were trailing 3-1 in the second period when George Parros and Peter Mueller each tallied to forge a tie before the frame was over.
Then with 10 1/2 minutes left in the third, the Sabres' Christian Ehrhoff was called for hooking, and Campbell converted a pass from Tomas Kopecky on the subsequent power play to provide the decisive score.
Shawn Matthias also found the net while Jose Theodore turned aside 17-of-20 shots as Florida logged a second straight win followed a five-game skid.
Leading NHL scorer Thomas Vanek netted his eighth of the year and added two assists for Buffalo, which lost for the sixth time in seven outings.
Ryan Miller made 29 saves for the Sabres.