Two goals in the first seven minutes of the second half put Japan on course to reach their first World Cup quarter-final before Roberto Martinez's game-changing substitutions.
Jan Vertonghen pulled one back for the Red Devils with a fluke header, and replacements Marouane Fellaini and Chadli saved the well-fancied Europeans in dramatic fashion to set up a quarter-final with Brazil.
Japan showed that they were not simply going to sit back when Shinji Kagawa unleashed a second-minute sighter which he dragged only a few yards wide of the post.
The Blue Samurai were the better team for the opening 20 minutes, harrying the Red Devils midfield relentlessly and passing their way through Belgian's own attempts to press.
However, the star-studded favourites went through the gears as the half-hour mark approached and had a series of chances to take a first-half lead.
Dries Mertens set up Romelu Lukaku for a close-range tap in but the Manchester United striker got his feet in a tangle, as did Kevin De Bruyne when he was teed up for a 20-yard shot with Mertens again involved.
Japan goalkeeper Eiji Kawashima was called into action for the first time when Eden Hazard unleashed a left-footed drive which he tipped around the post on 28 minutes, and his flap at the resultant corner went unpunished as nobody could get on the end of Vincent Kompany's full-stretch cutback.
Just as it appeared as though the number-three ranked side in the world were taking control, Japan showed their spirit as Yuto Nagatomo stood up a cross that striker Yuya Osako headed straight at Thibaut Courtois.
The Chelsea goalkeeper nearly embarrassed himself on the stroke of half time when he let a deflected Nagatomo shot through his legs, with only a despairing dive preventing the ball from sneaking over the line.
It was the whole Belgium team who were facing humiliation seven minutes into the second half as Japan opened up a surprising lead through two high-quality goals.
The build-up and finish for Japan's second was even better as Kagawa's silky footwork set up a shooting chance for Takashi Inui, who arrowed a shot across Courtois and inside the post to send his team into dreamland.
Although Hazard struck the post in the four minutes between the two Japanese goals, Belgium's response to conceding their second was a while coming and it took Martinez's intervention to salvage their tournament.
Lukaku's glaring miss on 62 minutes, when he glanced Thomas Meunier's cross wide with the goal gaping, could have been a key moment had Vertonghen not struck lucky with his own header seven minutes later, an attempt to direct the ball back into the danger zone which looped over Kawashima and underneath the crossbar.
Fellaini was thrown on to cause aerial carnage against a much smaller Japanese back line and did exactly that on 74 minutes when he powered the ball down and through Kawashima from Hazard's wicked delivery.
In fact, it was Japan's ambition to win the game without extra time which proved to be their downfall as they were caught on the break from their own 94th-minute corner, with Lukaku intelligently allowing Meunier's cross run to Chadli for a simple yet dramatic tap-in six yards out.
Belgium's two-goal comeback is the first in the knockout stages of the World Cup since 1970, and may give them the belief that they can go all the way, although they will have to go through Neymar and co. next.
BELGIUM (3-4-3): Courtois; Alderweireld, Kompany, Vertonghen; Meunier, Witsel, De Bruyne, Carrasco (Chadli, 65'); Mertens (Fellaini, 65'), Hazard, Lukaku
JAPAN (4-2-3-1): Kawashima; H. Sakai, Yoshida, Shoji, Nagatomo; Hasebe, Shibasaki (Yamaguchi, 81'); Haraguchi (Honda, 81'), Kagawa, Inui; Osako