The Clarets produced the classic little and large show to earn a priceless win in their bid to stay on the big stage.
Sean Dyche’s men were in danger of getting sucked nearer the Premier League’s relegation dogfight when they trailed in the manager’s 300th league game in charge of the Clarets to a goal from Burnley-born Harvey Barnes.
And even after a ninth goal of the season from top scorer Chris Wood had levelled the scores early in the second half, the Clarets were faced with the prospect of a worrying seventh home defeat of the campaign.
Instead, the towering figure of Pope kept out a Jamie Vardy penalty before pocket dynamo Westwood struck the winner with his first goal of the season - and first at Turf Moor - on what felt like a massive afternoon at Turf Moor.
A first home win since mid-December stopped the rot with the Clarets’ reward for a great show of character and courage a third victory in 10 league games and movement back up the table towards safety.
The Clarets were looking to avoid a fifth successive top-flight defeat for the first time since the 1975/76 season and re-establish some daylight between themselves and the bottom three.
Having been slow starters in their last two home games, Dyche’s men needed to be more positive against a Leicester side knowing an eighth away win would take them back level on points with Manchester City in second place in table.
And there’s no question the Clarets were greatly improved in a more positive approach that contributed to a wide-open first 45 minutes.
But, critically, Burnley couldn’t find the opening goal and for all their good intentions and decent passages of play only a long-range effort from Jay Rodriguez – back in the side following Ashley Barnes’ injury absence – forced Kasper Schmeichel to make a save.
Leicester, for their part, looked to strike on the break with their movement and forward options giving Burnley’s back line a test they passed for the first 35 minutes.
James Maddison should have made more of an early chance teed up by the elusive Jamie Vardy.
But the Clarets were dealing with the threat until Barnes pounced to put Leicester in front.
Dennis Praet nicked the ball off Jack Cork in midfield and when he released Barnes, the England Under-21 international burst past Ben Mee before drilling a low shot past Pope to punish his hometown club.
The Clarets needed a response but also a big save from Pope to keep them in the contest two minutes into the second half when he flew to his right to keep out an effort from Praet.
And almost immediately Burnley went closest yet to a goal when Charlie Taylor delivered a fine cross and Wood climbed well to steer a header just over the bar.
Wood wouldn’t be denied for long, though, and with 55 minutes gone the former Leicester man grabbed the equaliser to lift Turf Moor.
He scored against the Foxes in the reverse meeting – when a controversial late VAR decision had denied Burnley a point – and repeated the trick with a classic poacher’s effort he nudged over the line after Schmeichel had saved a Mee header from Dwight McNeil’s corner.
The momentum was with the Clarets, but Leicester had a golden opportunity to grab it back with just over 20 minutes to go when Barnes out-foxed Mee with a sublime first touch and turn of pace that earned him a penalty when brought down by the Clarets’ skipper.
The obligatory VAR check perhaps did nothing to help Vardy’s composure, but it still needed an excellent save from Pope, going to his left, to keep out the spot-kick and the scores level.
Vardy had a chance to make amends when he was slipped in by a fine pass from substitute Kelechi Iheanacho but again Pope was too big a barrier to pass, standing tall to block his fierce drive.
And within minutes the Clarets had grabbed a winner through Westwood as the midfielder’s desire to get into the penalty area paid off.
Taylor, having another fine game, once more delivered a cross which Jonny Evans could only slice into the air for Westwood to arrive and meet the ball on the bounce with a wonderfully measured finish which he guided past Schmeichel from 10 yards out.
The Clarets then had to dig deep to see it out and in a throw-back to their resilient best stood strong to secure a priceless victory which lifted them to 14th place in the table.
Burnley: Pope; Bardsley, Tarkowski, Mee, Taylor; Hendrick, Westwood, Cork, McNeil; Wood (Lennon 90), Rodriguez. Substitutes: Hart, Lowton, Brady, Pieters, Vydra, Long.
Leicester City: Schmeichel; Pereira, Evans, Soyuncu, Fuchs; Praet (Tielemans 74), Mendy; Perez (Iheanacho 74), Maddison, Barnes; Vardy. Substitutes: Ward, Justin, Morgan, Gray, Albrighton.
Referee: Anthony Taylor