Goals from Cristiano Ronaldo and Wayne Rooney were enough to secure victory for the Premiership stars. They also created more than enough chances to have stretched the scoreline with better finishing.
But Exeter took the game to United after the break and made life extremely difficult for their illustrious visitors for long periods of the game.
It was an almost surreal sight for the long-suffering City supporters that were packed into St James Park to see the likes of Rooney, Gary Neville, Ryan Giggs, Paul Scholes and Ronaldo running out of the tunnel.
Ronaldo opened the scoring in the ninth minute when he struck a low shot into the bottom corner after being picked out by Scholes inside the box.
City keeper Paul Jones then pulled off a great stop to deny Rooney after he was found inside the box by Eric Djemba-Djemba.
United always looked liked increasing the scoreline and Giggs headed Ronaldo's cross inches wide.
Rooney and Ronaldo both had shots charged down as Exeter defended desperately.
But the Grecians grew in confidence as they weathered the storm and might have grabbed an equaliser on the stroke of half-time. Sean Devine met Alex Jeannin's cross and his powerful volley drifted inches past the post with Tim Howard beaten.
Exeter started brightly after the break and forced United back for the first time in the match. Andy Taylor's fine cross was well held by Howard as Steve Flack prepared to pounce.
The Grecians had a fine second half and even looked the better side at times.
Midway through the half Taylor's curling free-kick was well-saved by Howard and Devine's close-range strike was ruled out for offside.
Rooney blazed over for United after he was put clean through by Darren Fletcher and Ronaldo also struck the ball over the bar from Rooney's cross.
Rooney finally made it two with four minutes left on the clock with a low strike after he was picked out by Quinton Fortune.
It was an extraordinary effort by the Grecians and the massive applause that rang around the ground at the final whistle said it all.