Corne had been the hero in round three against Stevenage and further etched his name into Stones folklore with a fine second-half finish to send George Elokobi's National League South side into the fifth round of the competition.
Stones were indebted to goalkeeper Lucas Covolan, who made a string of saves before Lamar Reynolds excellent 43rd-minute lob dared the 4,472-travelling fans from Kent to dream.
Jeremy Sarmiento levelled for Ipswich at the start of the second half, but the Championship club were toppled when Corne rifled home with 24 minutes left at Portman Road to continue the fairytale run of the sixth tier side.
Maidstone had banked £231,375 in prize money on their way to the fourth round and while they had already knocked out League Two and League One opposition, Ipswich were a step up in class.
— Emirates FA Cup (@EmiratesFACup) January 27, 2024
Town boss Kieran McKenna made 10 changes from Monday's draw at fellow promotion hopefuls Leicester, but it was still one-way traffic early on.
Brighton loanee Sarmiento hit the post from 25 yards and Omari Hutchinson's follow-up effort was saved by Stones goalkeeper Covolan inside five minutes. Hutchinson was in the thick of the action and struck the woodwork soon after before Brazilian stopper Covolan thwarted Cameron Humphreys.
An intriguing battle between Chelsea youngster Hutchinson and Covolan had already developed with his next left-footed effort parried wide.
This was all before the 15-minute mark and while Ipswich's relentless waves of attack momentarily calmed, Sam Morsy, Hutchinson and George Edmundson all squandered opportunities before Maidstone's strong support were able to get excited for the first time.
Liam Sole's lively run eventually came to nothing before a Gavin Hoyte cross was easily cleared, but it gave the support of the National League South club something to shout about.
Chants of 'Championship, you're having a laugh' soon followed, although Sarmiento nearly silenced them in the 35th minute. He glided past one challenge and then another before his long-range strike deflected off Paul Appiah and flicked the roof of the net.
Sone Aluko was the next guilty party for Ipswich when he scuffed wide after Dominic Ball's mishit, but it still felt a matter of time before the opener arrived.
It duly did with 43 minutes played although astonishingly went to the non-league outfit. Maidstone broke from a corner and Sole produced a wonderful lofted pass through to Reynolds, who collected and sumptuously scooped over Christian Walton with his left foot from 18 yards to spark pandemonium.
Stones boss Elokobi kept his cool, but the rest of his staff bundled Reynolds as the away fans jumped for joy.
Half-time followed and while Ipswich had enjoyed 78 per cent possession and were 18-1 up on the shot count, it was Maidstone who held the lead. Elokobi spent some of the interval being interviewed by BBC, but Ipswich hit back in the 56th minute.
After Stones centre-back Appiah had a pass intercepted, the hosts punished the visitors' out-of-position defence with Jack Taylor finding Sarmiento, who curled into the corner for his second goal since arriving on loan this month.
All eyes were now on if the fairytale run of sixth-tier Maidstone would crash to juddering halt but third-round hero Corne had other ideas.
It was Sarmiento who gave away possession to Reynolds by the halfway line and Stones scorer turned creator with a pass into Corne, who impressively held off Edmundson and rifled home from 12-yards with 24 minutes left.
McKenna watched Ipswich substitute Harry Clarke test Covolan before Wes Burns fired wide and Edmundson was then booked for simulation in the 76th minute after going down with Manny Duku in close proximity.
Ipswich pushed for one last chance and their big moment arrived with six minutes left, but Conor Chaplin's bundled effort was brilliantly tipped onto the crossbar by Covolan to ensure Maidstone progressed into the fifth round.