United had fallen behind to Ademola Lookman's opener at St. James' Park, but Guimarães scrambled in an equaliser – his first goal at the Magpies' home – to ensure his side went into the break on level terms.
A nervy second half looked set to end evenly until the 95th minute, when substitute Joe Willock set off on a terrific individual run before crossing for Guimarães to seal all three points with a diving header in front of the Gallowgate End. It was Newcastle's latest-ever winning goal in the Premier League era, and a magnificent finish to another superb display from the January signing.
Centre back Burn – who turned in a solid showing at the heart of United’s defence – paid tribute to his teammate after that breathless finale against the Foxes.
"Bruno's shown his quality and why we've paid the money for him. He deserves all the plaudits," Burn told nufc.co.uk. "I love all the flair he's got, but it's the other side that I appreciate – the tracking back, the recovery runs, the tackling, and then making it into the box in the last minute.
"I think all the lads in front of us have been brilliant, but Bruno was great today. I think he feeds off the crowd, so with the crowd behind him he's been an instant cult hero. He deserves everything he's got today. I thought he was brilliant."
Lookman's opener after a well-worked corner routine, a goal which the Burn felt was conceded in "disappointing" fashion, was the only blemish on an otherwise memorable afternoon for Eddie Howe's men.
The former Brighton man admitted that his side were a little below par during spells of the contest – but he feels that going on to secure the victory in such circumstances "shows the signs of a good team".
"It was crazy. I don't think we were at our best today. But I think it's a good sign that we weren't at our best, and we're still picking up results," he said.
"I think with about five minutes to go we probably would have settled for a point, but the determination from Willo (Joe Willock) to run that ball down the line and get that ball in the box… he's done nothing wrong to not be in the team, it's just the way that we're playing at the moment. I think it just sums up the squad and the place where we're at at the minute.
"I think that shows the signs of a good team, when you can not perform at your best and still pick up points and wins. We're heading in the right direction, but it's not done yet – we’ll just keep fighting until it is."
The win takes United 12 points clear of the relegation zone ahead of Wednesday night’s visit of Crystal Palace.
With the triumph over the Foxes in the bag, Burn could allow himself to laugh off his missed chance at the Gallowgate End when he was picked out in the second half – but the Ashington-born stopper insists a first goal for his boyhood club won't be too far away.
"I probably got up about ten seconds too early," rued the 29-year-old, after failing to connect properly with Matt Targett’s cross. "I will get one, I promise – it's coming. I'm getting in the positions to score now, so it's just a matter of time."
