The Foxes, who set out in a 3-5-2 formation from the off, made a bright start to the contest without truly troubling Jon McLaughlin.
Burton included three triallists in their starting lineup, and it was one of those looking to impress boss Jimmy Floyd Hasselbaink who came closest to opening the scoring 17 minutes in, with a shot that Kasper Schmeichel got across well to save.
A lively Andrej Kramaric tested McLaughlin up the other end from long range, while Vardy could not quite get the better of the Brewers stopper when in behind.
The closest either side came to making a breakthrough in the first half came shortly before the interval, when Andy King saw his shot from 25 yards out come back off the upright.
Former Leicester youngster George Taft headed over the first chance of the second 45 minutes, just moments before Vardy lifted a shot over the bar from 12 yards out.
Calum Butcher was the next Burton player to try his luck as he rattled the crossbar with a long-range drive, but the game's opening goal finally arrived when Vardy curled the ball home from a narrow angle just after the hour.
The visitors continued to knock on the door, and they were rewarded with a second thanks to Vardy's well-taken header at the end of Marc Albrighton's cross.
Just moments after Vardy had been denied a hat-trick by a good McLaughlin stop, Burton managed to pull a goal back at the death through substitute Mark Duffy's curled strike into the far corner.