The Red Devils were 50/1 (51.0) with bet365 even before they lost the first leg 2-0 at Old Trafford and that price was drifted to 125/1 (126.0) following the reverse in Manchester.
However, despite missing a host of players including Paul Pogba, Ole Gunnar Solskjaer led his team to the most spirited of performances – with Marcus Rashford securing their quarter-final spot courtesy of a 94th-minute penalty.
Dusan Tadic turned in a masterclass to lead the Dutch outfit past the reigning champions and Ajax are now 20/1 (21.0) to win the tournament - after being as long as 200/1 (201.0) following the first leg.
Those two heavyweights being knocked out at this relatively early stage means Manchester City are just 5/2 (3.50) to claim a maiden Champions League crown this season.
The Premier League leaders welcome 500/1 (501.0)Schalke to the Etihad Stadium next Tuesday with a 3-2 advantage following Raheem Sterling’s late winner in Germany.
Barcelona are available at 4/1 (5.0), having been shortened from 5/1 (6.0) in recent days thanks to the eliminations of Real Madrid and PSG.
bet365’s Steve Freeth said: “It would be a major surprise if 1/150 shots Man City didn’t make the last eight, while Liverpool travel to Munich as slight favourites to qualify, so four English quarter finalists is a real possibility – just like in 2007/8 when Chelsea and Man Utd contested the final in Moscow.”
The Reds are 9/1 (10.0) and Bayern slightly further out at 10/1 (11.0) to win the Champions League, whilst Porto can be backed at 66/1 (67.0) despite overcoming last season’s semi-finalists Roma on Wednesday night.