The Clarets had found some form of late – picking seven points up out of the last nine available – but they never fully got going against the Midland-based outfit.
Neither Maddison or Vardy were named in the starting line-up but both delivered goals in the final ten minutes to earn Leicester their first Premier League victory of 2022 – no doubt delighting manager Brendan Rodgers.
Story of the match
Despite battling valiantly for a point against Crystal Palace, Burnley boss Sean Dyche wielded the changes. Maxwel Cornet, Ashley Westwood and Charlie Taylor came in for Jay Rodriguez, Jack Cork, and the injured Erik Pieters.
Caglar Soyuncu came back into the team alongside fit-again Ricardo Pereira, while Kiernan Dewsbury-Hall returned to the midfield. Patson Daka lead the attack while Vardy made the substitute's bench after a lengthy lay-off.
The PA system at Turf Moor had broken so everybody in attendance was treated to a surreally naturalistic sound, bustling throughout the stadium. No music. No line-up announcement. No announcements full-stop.
There was something quite fitting about that, as players warmed up with t-shirts that demonstrated their support for Ukraine at this terrible, terrible time. Some things are far bigger than football.
Burnley started brightly in a territorial sense but it was the visitors who let off the first shot in anger on the fifth minute – Youri Tielemans lifting a 25-yard effort over the bar after sauntering down the centre of the pitch without a challenge.
That shot prompted a shift in early momentum and the Foxes began to up the intensity.
Periera twisted and turned away from two Burnley challenges before forcing Nick Pope into a stunning low stop, down to the goalkeeper's right. The Portuguese star then miscued a volley on the edge of the box after a half-cleared corner. It was certainly a lively opening for the full-back on his return from injury.
The home stopper was called into action again on 18 minutes following a mistake from James Tarkowski, sticking out a leg to deny keep out an angled strike from Daka.
It was a bit of a wake-up call for the Clarets and they thought they had provided the perfect tonic when Cornet tapped into an empty net after brilliant play from Aaron Lennon. Unfortunately for the Ivorian, he had strayed narrowly offside.
And the substitute was immediately in the thick of the action, getting turned by the speedy Harvey Barnes – whose thunderous shot from inside the box was parried over by Pope.
Not for the first time this season, the hosts seemed fired up after their half-time team-talk and Connor Roberts was quick to force Kasper Schmeichel into his first meaningful save with a cross-cum-shot that the Dane had to push to safety.
Leicester also had to replace Pereira during the interval, presumably due to injury, so that wasn't an ideal preparation for the second 45 minutes.
However, it didn't take long for the Foxes to regain their footing and – despite not creating too many clear openings – they kept Schmeichel Twell protected.
Burnley did almost carve through on 69 minutes, though, as McNeil prodded Cornet in on Schmeichel but the club's top scorer couldn't get a clean strike off with Soyuncu closing down his space. It was the last action of the match for Cornet, who was replaced by Rodriguez just moments later.
Rodgers reacted with a double switch himself: throwing Vardy and Maddison into the mix at the expense of Daka and Tielemans.
Vardy did look to have a clear sight of goal when he left Collins on the floor but the 35-year-old stumbled over at the vital moment.
Barnes then forced Pope into a brilliant one-handed stop with an effort from just outside the area. It seemed like the visitors were up against an immovable object between the sticks.
However, that last-line of resilience didn't last forever and the Foxes were rewarded in the final eight minutes.
The two substitutes combined as Vardy knocked Schmeichel's long punt pass back to Maddison and the midfielder wasn't picked up by anyone in claret and blue. He had all the time in the world to shape up an angle before bending the ball into the far corner from just outside the box.
It was a hammer blow for the Clarets but they nearly snatched a quickfire equaliser when Wout Weghorst prodded a whipped in corner narrowly wide at the back-post.
Dyche threw Ashley Barnes on as a last throw of the dice but that only opened up gaps at the back for Leicester to exploit. And they did.
The menacing Harvey Barnes whipped a quick delivery across the six-yard box and Vardy was on-hand to nod the ball in from point-blank range. Game set and match just before the ninety minute mark.
It's a result that leaves Burnley just one point away from the drop zone while Leicester move up to 12th.