Barnsley have advanced to the fourth round of the FA Cup for the first time since 2012-2013, they had lost each of their past five third round ties.
Barnsley have now scored 11 goals in their past four FA Cup ties.
Jacob Brown fired Barnsley in front after three minutes, the Reds earliest FA Cup goal since February 2013 when Chris Dagnall also scored after three minutes in a 3-1 win at MK Dons in the Fifth Round.
Since that Dagnall strike Barnsley have scored 23 FA Cup goals with 16 of them coming in the second half.
It is only the third time in six years Barnsley have opened the scoring in the third round - with the side going on to LOSE on the two previous occasions (4-1 to Millwall in 2017-2018 and 2-1 to Coventry in 2013-2014)
The Reds have however opened the scoring in three of their last four FA Cup ties, only failing to do so at Burnley in last season's third round.
Barnsley led at half-time for the first time in nine FA Cup ties, last doing so in a second round replay at Chester in December 2014.
Barnsley have kept only two clean sheets in their last nine FA Cup ties (against Notts County and Blackpool) however they would lose the replay to Blackpool.
Conor Chaplin scored his eighth goal in 11 games and only his second ever in the FA Cup having netted for Portsmouth in a 2-2 draw at Ipswich in the third round in 2016.
It is Chaplin's ninth goal of the season, his second best ever scoring season behind only the 11 he scored in 38 games for Portsmouth in 2015-2016 (he had eight after 26 games that season compared with nine from 26 in 2019-2020)
He also assisted Brown's opener, meaning he has been involved in 11 goals in the last 11 games (8 goals, 3 assists)
It was the fifth time this season a player has both scored and assisted in a game (Chaplin 2, Woodrow, Mowatt and Bahre)
Barnsley scored in both the first five and last five minutes of a match (3, 90+4) for the first time since February 2019 when they scored in the first minute and injury time at Gillingham.
Luke Thomas' breakway third goal was the Reds sixth 90+minute goal this season.
There has been a 90+minute goal in six of Barnsley's last nine games.
Brad Collins finally had his first win between the post for the Reds, they had drawn five and lost seven of his 12 previous appearances.
Barnsley ended a run of five matches without a win on a Sunday (D1 L4), prior to this game their last Sunday success was in the League One Play-Off Final in May 2016.
This was the first FA Cup encounter between Crewe and Barnsley since January 1927, when the Reds won 6-1, also in the third round.
Barnsley have now progressed from their three FA Cup meetings with Crewe, doing so in 1905-06 and 1926-27.
Barnsley have now won four of the last five meetings with Crewe (all comps)
They have also won three successive games at Gresty Road for the second time ever.
Crewe have now failed to reach the FA Cup fourth round for 18 years, last doing so in 2002.
Barnsley meanwhile have reached the fourth round for just the third time in 22 seasons.
This was Barnsley's first win in six FA Cup ties as a Championship team (D1 L4).
Crewe had 57% possession in the game, the first time the Reds have not had the majority of ball possession against a team this far down the football pyramid since non league Chester enjoyed 55% in a second round replay, which Barnsley won 3-0 in 2014.
It is the first time Barnsley have conceded the majority of possession in a third round tie since that same 2014-2015 season when Middlesbrough had 61% as they won 2-0 at Oakwell.
It is only the second time this season Barnsley have won when they have not had the majority of possession - also doing so against Fulham on the opening weekend of the season (45%)
Barnsley scored three goals away from home for the first time since April, at Plymouth.
Bambo Diaby picked up his eighth booking of the season - and fourth in five games.
40. Brad Collins
2. Jordan Williams
4. Kenny Dougall
5. Bambo Diaby
6. Mads Andersen
7. Jacob Brown
16. Luke Thomas
22. Clark Oduor
27. Alex Mowatt (c)
28. Elliot Simoes
19. Patrick Schmidt (for Simoes 72)
3. Ben Williams (for Oduor 78)
1. Samuel Radlinger, 10. Mike-Steven Bähre, 20. Callum Styles, 21. Toby Sibbick, 24. Aapo Halme.
1. Will Jaaskelainen
2. Perry Ng (c)
3. Harry Pickering
4. Ryan Wintle
7. Daniel Powell
10. Charlie Kirk
11. Callum Ainley
12. Paul Green
15. Nicky Hunt
16. Tom Lowery
17. Chuma Anene
19. Owen Dale (for Kirk 76)
14. Oliver Finney (for Ainley 82)
8. James Jones, 13. Dave Richards 23. Travis Johnson, 25. Rio Adebisi, 30. Christian Mbulu.
Crewe manager Dave Artell said:
"I thought the first half was nip and tuck. We should have gone in 1-1. We got the goal but then after that they have imposed themselves far greater than we have and they have deserved to win in the end.
"It's a disappointing day. I don't think there was much to choose between the two teams at times and then at other times I thought Barnsley did a really good job. We will lick our wounds and go again."
FA Cup Third Round results:
SATURDAY 4TH JANUARY 2020
Bristol City 1-1 Shrewsbury Town
Millwall 3-0 Newport County
Mahoney pen 64
Rochdale 1-1 Newcastle United
Rotherham United 2-3 Hull City
Birmingham City 2-1 Blackburn Rovers
Armstrong pen 61
Burnley 4-2 Peterborough United
Brighton & Hove Albion 0-1 Sheffield Wednesday
Cardiff City 2-2 Carlisle United
Fulham 2-1 Aston Villa
Oxford United 4-1 Hartlepool United
Taylor pen 87
Southampton 2-0 Huddersfield Town
Brentford 1-0 Stoke City
Preston North End 2-4 Norwich City
Idah pen 61
Reading 2-2 Blackpool
Watford 3-3 Tranmere Rovers
Mullin pen 87
AFC Bournemouth 4-0 Luton Town
Leicester City 2-0 Wigan Athletic
Pearce og 19
Wolverhampton Wanderers 0-0 Manchester United
Fleetwood Town 1-2 Portsmouth
Manchester City 4-1 Port Vale
SUNDAY 5TH JANUARY 2020
Charlton Athletic 0-1 West Bromwich Albion
Chelsea 2-0 Nottingham Forest
Crewe Alexandra 1-3 BARNSLEY
Middlesbrough 1-1 Tottenham Hotspur
Lucas Moura 61
Queens Park Rangers 5-1 Swansea City
Sheffield United 2-1 AFC Fylde
Bristol Rovers 2-2 Coventry City
Clarke-Harris pen 6
Craig og 53
Burton Albion 2-4 Northampton Town
Crystal Palace 0-1 Derby County
Liverpool 1-0 Everton
Gillingham 0-2 West Ham United
MONDAY 6TH JANUARY 2020
Arsenal 1-0 Leeds United
Sky Bet Championship Matchday Twenty Seven: Barnsley v Huddersfield Town, Saturday 11th January 2020. Kick-Off: 3pm
On The Road:
Sky Bet Championship Matchday Twenty Eight: Bristol City v Barnsley, Saturday 18th January 2020. Kick-Off: 3pm