Jackson scored on a 9-yard run in the second quarter and backup quarterback Thad Lewis tossed for 193 yards with an interception as the Bills (6-9) won a second straight.
Starting signal-caller EJ Manuel was held out of the game with a knee injury.
Dan Carpenter booted four field goals and the Buffalo's defense recorded seven sacks en route to the victory.
Ryan Tannehill was limited to 82 passing yards on 10-of-27 efficiency for the Dolphins (8-7), who had won three straight entering the game but blew a chance to clinch their first playoff berth since 2008 with a victory.
With Miami's loss, New England won its fifth straight AFC East title.