The result leaves Arsenal in fifth place on 15 points, two behind Leicester City and Chelsea, while Sheffield United moved into ninth on 12 points.
United looked dead and buried as they struggled to get back into the contest after the break but 19-year-old Brandon Williams's first senior goal 18 minutes from time sparked them into life. However, substitute McBurnie denied the visitors in stoppage time to add a further twist to the breathless encounter, squeezing a strike past De Gea, with the goal awarded after a lengthy VAR review.
Liverpool survived a late spell of Everton pressure to stretch their record unbeaten run in Merseyside derbies to 17 games
A dreadful defensive error from Arsenal's Granit Xhaka gifted Burnley an equaliser as the sides drew 1-1 at Turf Moor in the Premier League on Saturday.
Aaron Ramsey scored a hat-trick on Saturday as Arsenal thrashed Everton 5-1 in the Premier League at the Emirates with a display of free-flowing football that the Gunners have sorely lacked away from home this season.
James Maddison scored a brilliant winner to help Leicester City come from behind and beat Tottenham Hotspur 2-1 in the Premier League on Saturday in a match dominated by VAR drama.
Sheffield United's David McGoldrick scored twice as they stunned Chelsea with a 3-0 win at Bramall Lane on Saturday, loosening the visitors' grip on a Premier League top-four place. Raheem Sterling struck a hat-trick as Manchester City crushed Brighton 5-0 at the AmEx Stadium in the Premier League on Saturday.
Marcus Rashford scored twice as Manchester United extended their 100 percent record on the road, coming from behind again to win 3-2 at the English Premier League's bottom club Sheffield United on Thursday.
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Manchester City paid the price for missed chances as they were held to a 1-1 draw at Burnley on Saturday with Johann Berg Gudmundsson's 82nd minute equaliser earning the hosts a share of the points.
IMAGES from the English Premier League match played on Saturday
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Manchester City made sure of third place in the Premier League when they romped to a 5-0 win at Watford on Sunday to ensure a Champions League berth for next season.