A 92nd minute penalty denied Barnsley the chance to make the FA Cup Fourth Round for the first time since 2012-2013.
It also means that since beating Chelsea in the 2007-2008 Quarter-Final, the Reds have lost their last five FA Cup matches against Premier League opposition by an aggregate score of 2-15. (Burnley 0-1, Manchester City 0-5, Swansea 2-4, West Ham 0-2, West Ham 0-3)
However this was the first one of those five where Barnsley went in at half-time level.
It is the second time in a row that Barnsley have been level against a Premier League team at half-time after also being goal-less with Tottenham in the League Cup last season.
This was the first time Barnsley have lost a match in injury time since the 23rd September 2017 when a 93rd minute Alfred N'Diaye strike secured a 2-1 win for Wolves at Molineux.
VAR was used in a Barnsley game for the first time ever and it reversed a first half penalty decision initially given for a foul by Dimi Cavaré on Madej Vydra however it was overturned as Vydra was offside. It is though the first time Barnsley have conceded two penalties in one game since August 2016 against QPR.
Remarkably Burnley were awarded two penalties in one match having gone 64 games without being awarded one last doing so in the League Cup in September 2017 - this was also converted late on by Chris Wood (89th) and against a Yorkshire opponent (Leeds)
Wood who had a fairly forgettable loan spell at Oakwell in 2010 - failing to score in seven appearances - has scored in his last two appearances against the Reds, including netting a double for Leeds at Oakwell in January 2017 - with one also being a penalty.
Wood has now scored four goals in the third round for four different teams - West Brom, Brighton, Leicester and Burnley.
Each of the last three meetings with Burnley have now finished 1-0 with the Clarets winning all three.
Four of the last six have also finished with this scoreline and that includes Barnsley winning an FA Cup Third Round tie in 2013.
No team has scored more than once in any of the last six meetings with Burnley being the last team to do so in 2012.
There was 11,053 in attendance at Turf Moor - the lowest crowd at the ground for a FA Cup tie since January 2015 (9,348) - surprisingly the opponents were Tottenham.
Ryan Hedges made only his fifth start of the season and the first since November.
Barnsley have gone back to back games without scoring for the first time this season and the first time since December 2017.
It is the first time they have failed to score in their first two games of a calendar year since 2009 when they failed to score in their first three.
The Reds have now won just one of their last 11 visits to face Burnley at Turf Moor in all competitions (D2 L8), winning 2-1 in the Championship in December 2008.
Burnley have now lost just one of their last nine home FA Cup games (W7 D1)
This is the tenth time a Barnsley match has been goal-less at half time this season
Despite playing a Premier League side Barnsley enjoyed the majority of the ball possession (52%) - for the 32nd time this season
Burnley had 11 shots, the most by an opponent since Bristol Rovers also had 11 in October, however only two of those were on target including the penalty winner.
Barnsley themselves had nine efforts, but failed to manage a single shot on target for the first time this season.
1. Adam Davies (c)
12. Dimitri Cavaré
5. Ethan Pinnock
6. Liam Lindsay
28. Ben Williams
8. Cameron McGeehan
7. Ryan Hedges
27. Alex Mowatt
21 Mike-Steven Bähre
26. Mamadou Thiam
25. Cauley Woodrow
19. Kieffer Moore (for Hedges 63)
10. George Moncur (for Thiam 77)
4. Kenny Dougall (for Bähre 83)
18. Adam Jackson, 29. Victor Adeboeyjo, 33. Jacob Brown, 35. Jake Greatorex
29. Nick Pope
5. James Tarkowski (c)
28. Kevin Long
14. Ben Gibson
23. Stephen Ward
31. Dwight McNeil
16. Steven Defour
13. Jeff Hendrick
3. Charlie Taylor
27. Matej Vydra
9. Sam Vokes.
7. Johann Berg Gudmundsson (for Ward 59)
11. Chris Wood (for Vokes 74)
4. Jack Cork (for Defour 78)
6. Ben Mee, 10. Ashley Barnes, 18. Ashley Westwood, 20. Joe Hart.
Burnley manager Sean Dyche said:
"We've pieced together a side and I'm pleased because that was a good Barnsley side.
"I felt we had enough to win the game and did enough to win the game, especially at the end of a big, important week for us.
"I'm a big advocate of VAR but the referee needs to hold the ball. I know they want to be right, but they do need to speed it up and those things will get ironed out.
"The referee allowed the set-up for a penalty and I know we are learning about it, but the referee should grab the ball and walk outside the penalty area, so there are no implications.
"Matej had got to the point of his run-up before the referee blew his whistle and said 'no'.
"That delay was what annoyed me - not the outcome - because once you know that is right you quickly move on."
FA Cup Third Round results:
Friday 4th January 2019:
Tranmere Rovers 0-7 Tottenham Hotspur
Son Heung-Min 57
Saturday 5th January 2019:
AFC Bournemouth 1-3 Brighton & Hove Albion
Burnley 1-0 BARNSLEY
Wood pen 90+2
Manchester United 2-0 Reading
Mata pen 22
Sheffield Wednesday 0-0 Luton Town
Shrewsbury Town 1-1 Stoke City
Norburn pen 45+4
West Bromwich Albion 1-0 Wigan Athletic
West Ham United 2-0 Birmingham City
Accrington Stanley 1-0 Ipswich Town
Aston Villa 0-3 Swansea City
Bolton Wanderers 5-2 Walsall
Guthrie og 63
Beevers og 68
Brentford 1-0 Oxford United
Maupay pen 80
Chelsea 2-0 Nottingham Forest
Derby County 2-2 Southampton
Everton 2-1 Lincoln City
Fleetwood Town 2-3 AFC Wimbledon
Evans pen 72
Gillingham 1-0 Cardiff City
Middlesbrough 5-0 Peterborough United
Blackpool 0-3 Arsenal
Bristol City 1-0 Huddersfield Town
Crystal Palace 1-0 Grimsby Town
Newcastle United 1-1 Blackburn Rovers
Ritchie pen 84
Norwich City 0-1 Portsmouth
League One results:
Charlton Athletic 1-1 Sunderland
James og 50
Rochdale 0-4 Burton Albion
Scunthorpe United 2-1 Coventry City
Sunday 5th January 2019:
Fulham 1-2 Oldham Athletic
Surridge pen 76
Manchester City 7-0 Rotherham United
Ajayi og 45+1
Millwall 2-1 Hull City
Preston North End 1-3 Doncaster Rovers
Queens Park Rangers 2-1 Leeds United
Oteh pen 23
Sheffield United 0-1 Barnet
Coulthirst pen 21
Woking 0-2 Watford
Newport County 2-1 Leicester City
Amond pen 85
Monday 6th January 2019:
Wolverhampton Wanderers 2-1 Liverpool
Barnsley drop to 5th place in Sky Bet League One with 46 points from 25 games. We are 2 points inside the Play-Offs, 6 points off the Automatic Promotion Places, 11 points off First Place and 19 points above the Relegation Zone.
Up to 06/01/19
Sky Bet League One Matchday Twenty Six: Barnsley v Bradford City, Saturday 12th January 2019. Kick-Off: 3pm
On The Road:
Sky Bet League One Matchday Twenty Seven: AFC Wimbledon v Barnsley, Saturday 19th January 2019. Kick-Off: 3pm