Ex-Don Ali Al-Hamadi gave the Blues a third-minute lead, but the League Two hosts hit back with goals from Omar Bugiel and Matty Stevens either side of the break to get Plough Lane rocking.
The party was in danger of going flat when Conor Chaplin levelled for the Tractor Boys on 86 minutes, but the Dons held their nerve to triumph 4-2 on penalties and earn a juicy third round tie at home against Newcastle.
Isaac Ogundere netted the winning spot-kick after Dons keeper Owen Goodman had saved from Jack Taylor and Omari Hutchinson.
"We said to the lads there will be no repercussions if it (the penalty shoot-out) doesn't go our way, so hopefully that brought them a bit of calmness," a delighted Jackson told BBC Radio London. "They took them really well.
"It's the highlight of my career, certainly one of them.
That's the third time coming up against Kieran (McKenna) as a manager and it hasn't gone great for me in the previous couple, so to win tonight against such a talented young coach is nice on a personal level.
"But I'm just really pleased for the football club to have a night like this. Beating a Premier League team is outstanding."
Fellow League Two side Barrow also took the scalp of higher level opposition, knocking out Championship newcomers Derby 3-2 on spot-kicks after a goalless draw. It took the Bluebirds through to the third round for the first time since 1967-68 and they can now look forward to a glamour trip to Chelsea.
After James Collins and Kayden Jackson missed their penalties for Derby, Barrow keeper Paul Farman saved from Craig Forsyth to seal the upset.
Denne historien er fra September 01, 2024-utgaven av The Football League Paper.
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Denne historien er fra September 01, 2024-utgaven av The Football League Paper.
Start din 7-dagers gratis prøveperiode på Magzter GOLD for å få tilgang til tusenvis av utvalgte premiumhistorier og 9000+ magasiner og aviser.
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LUKE BOOSTED BY WALES ACE LIAM
Swans bid to mark new era in style...
MATT'S DELIGHT OVER RECORD
WYCOMBE boss Wanderers Matt Bloomfield hailed his history-makers after victory at Lincoln City.
TON-UP IAN ENJOYS HIS SPECIAL WIN
AN Evatt described his 100th win as Bolton boss as very special, although he needed Aaron Collins' injurytime goal to bring up the three figures.
DONS LACK A CLINICAL EDGE AS SADDLERS GRAB POINTS
NATHAN Lowe's strike inspired promotion-chasing Walsall to victory over AFC Wimbledon at the Cherry Red Records Stadium.
SUB GRIMES IS IN-SPIRED TO HEAD THE WINNER
CAPTAIN Jamie Grimes headed in a late winner for Chesterfield after a game of very few chances appeared destined to remain goalless.`
COBBLERS TEST IN TROPHY FOR POSH
HOLDERS Peterborough United have been drawn against fellow League One side Northampton Town in the Round of 32 of the newly-named Vertu Trophy.
HORNETS REMINDED OF GRAY'S BRILLIANCE
WAYNE Rooney expressed his delight as Plymouth extended their unbeaten league home run to six after Andre Gray's last-gasp leveller.
MARTI DOUBTING JOB AFTER DRAW
Rangers home run continues
BIG MAC'S ON TARGET TO SEE OFF THE TIGERS
LUTON boss Rob Edwards felt it was a very good day at the office as his team turned in a gritty performance to beat Hull.
Rohl confident Owls
DANNY Rohl said getting results is the only thing missing as his Owls were held at home by Cardiff.