Prior to this encounter, Burnley had gone 29 Premier League matches without having kept a clean sheet.
What's more, the Clarets have never previously drawn a Premier League fixture 0-0 - this was their 41st outing.
As for visiting United, Louis van Gaal is still searching for his first competitive victory in charge of the Red Devils.
Manchester City 0-1 Stoke City
The defeat was only the second that Man City manager Manuel Pellegrini has suffered in the Premier League at the Etihad Stadium.
It was also only the second time in 71 home encounters that City had failed to find the net.
Before this fixture, Stoke had played 12 Premier League matches in Manchester against City and United and had lost all of them.
Newcastle United 3-3 Crystal Palace
Dwight Gayle's goal for Crystal Palace after 29 seconds was the quickest that has been scored in the Premier League this season.
Meanwhile, up the other end, Palace have conceded two or more goals in their last six matches.
After Patrick Kluivert and Vurnon Anita, Daryl Janmaat is the third Dutchman to have scored in the Premier League for Newcastle.
Queens Park Rangers 1-0 Sunderland
Charlie Austin's goal was the first scored by QPR in the Premier League this season.
His goal meant that visiting Sunderland have kept just one clean sheet in their previous 13 away encounters.
The Black Cats have now lost their last two matches against the R's. Prior to that, they had not been beaten by the West Londoners since 1991.
Swansea City 3-0 West Bromwich Albion
Swansea winger Wayne Routledge has scored his last eight goals for the club at the Liberty Stadium.
Meanwhile, Routledge's teammate Nathan Dyer found the net twice in a game for the first time since the opening day of the 2012-13 season.
Talking of goals - they have been hard to come by on the road for West Bromwich Albion, who have failed to find the net in their last four away matches.
West Ham United 1-3 Southampton
Mark Noble has now scored at least one goal in the last eight campaigns that West Ham have played in the Premier League.
However, the defeat means that West Ham have lost their first two home matches of the new term.
Two of Southampton's goals were scored by Morgan Schneiderlin, which is the same tally that the French midfielder managed during the whole of last season.
Everton 3-6 Chelsea
Diego Costa is the first Chelsea player to score in the season's opening three matches since Adrian Mutu in 2003.
Up the other end, former Chelsea striker Samuel Eto'o scored his first goal for Everton and his 10th in the Premier League. However, it was his first away from Stamford Bridge.
His teammate Steven Naismith, meanwhile, has scored in all three of Everton's Premier League matches this season.
Aston Villa 2-1 Hull City
Hull may have lost, but they have now scored in their five Premier League away matches.
As for Villa, Austrian winger Andreas Weimann has scored three times in his last two outings against the Tigers.
He has also been involved in all three of Villa's goal this season - two goals and an assist.
Tottenham Hotspur 0-3 Liverpool
Liverpool have now won their last three matches against Tottenham, with an aggregate score of 12-0.
The defeat was the first that Mauricio Pochettino had suffered since taking charge of the North Londoners in the summer.
Over the course of the 90 minutes, the hosts recorded just one shot on target.
Leicester City 1-1 Arsenal
Excluding own goals, Alexis Sanchez became the 100th player to score a Premier League goal for Arsenal.
However, the draw means that Arsene Wenger's side have won only three of their previous 10 away fixtures.
As for the Foxes, they have not got the better of Arsenal since a 2-1 victory at Filbert Street in 1994.
