United must now travel to St James Park for an unwanted replay the week after next and the FA Cup holders must raise their game considerably if they are to progress.
Manager Sir Alex Ferguson picked a team which looked weak even compared to his usual Carling Cup line-up.
And while United were dreadful, take nothing away from the side lying forth in the Nationwide Conference.
Roared on by their 9,000 following, Exeter even had chances to win and there was no greater compliment to the Devon side than Ferguson's decision to throw on Paul Scholes, Cristiano Ronaldo and Alan Smith in a desperate last throw of the dice.
Former Old Trafford youngster Andy Taylor almost put his heroes to the sword on the half hour.
United's Spanish youngster Gerard Pique's poor defensive header across his box set up Taylor to fire in a superb 20-yard shot which was brilliantly saved by diving goalkeeper Tim Howard.
Although that was Exeter's best effort, the Grecians also had a number of half chances.
Taylor fired one free-kick from the edge of the United box into the side netting, while the industrious Dean Moxey shot narrowly wide from 10 yards after Marcus Martin's pass caused havoc in the home penalty area.
Skipper Sean Devine's 25-yard drive in the 50th minute was deflected narrowly over his own bar by Wes Brown.
United had their chances and were denied on several occasions by the brilliance of Exeter goalkeeper Paul Jones and the magnificent defenders around him.
The Red Devils had a series of half chances earlier on, but it was not until midway through the first half that Jones had to make the first of a series of super saves.
Unsighted by players from both sides, the Exeter goalkeeper hurled himself across his line to touch away Chris Eagles' in-swinging free kick from 25 yards out on the left.
David Bellion headed another Eagles cross straight at Jones soon after, while United's best chance of the first half came three minutes before the interval.
Bellion curled in a free-kick from 25 yards which Jones again tipped away. The ball fell to Phil Neville whose cross from the right was headed narrowly over the bar by Eagles.
Former Manchester City defender Scott Hiley thwarted the old foe four minutes after the break.
A tremendous right-foot shot from impressive United youngster David Jones from the edge of the Exeter penalty area was superbly cleared off the line by Hiley.
Ferguson was forced to bring on Scholes and Ronaldo after 63 minutes and United began to look more of a threat.
Kieran Richardson twice fluffed close-range efforts and Ferguson played his last card in the 76th minute when Alan Smith replaced the ineffectual Bellion.
Within a minute, Smith was in the thick of the action, heading Neville's long pass into the path of Ronaldo on the right.
The Portuguese youngster produced a ferocious shot from 25 yards which was magnificently turned away by the acrobatic Jones.
Smith fired narrowly wide from close range soon after, while Scholes was inches short of the target two minutes into injury time following a good move involving Smith and Richardson.
MAN OF THE MATCH: Dean Moxey (Exeter) Gave the United defence problems with his quick thought and hard work. He almost caused an even bigger shock with one first half shot which went narrowly wide.