The Bills opened the scoring early on when Dan Carpenter kicked a field goal from 42 yards, but Josh Scobee soon restored parity with a 32-yard effort of his own.
The Jaguars took the lead right at the start of the second quarter when Chad Henne threw a short pass to Ace Sanders, who made his way past one defender on the outside before sidestepping another to complete a 12-yard score.
Buffalo levelled things up once again midway through the quarter when Robert Woods reached into the endzone after being found by EJ Manuel's seven-yard pass.
The visitors then ensured that they would go into the break in front when Manuel burst through the middle of the defense to run in for an eight-yard score of his own.
They then added to this lead with just two seconds left on the clock as Carpenter kicked a field goal from 40 yards to open up a 10-point gap at the break.