United remain at the League One summit with a game in hand despite the loss, although their lead has been cut to three points following Norwich's thrashing of Colchester.
Exeter thoroughly deserved their win and they signalled their intent by taking the lead with just four minutes played.
A delightful three-man move was started and finished off by Ryan Harley, the midfielder powering a close-range header past Casper Ankergren to give his side the lead.
Richard Duffy nearly gifted Leeds a leveller when he headed towards his own goal, but the Welshman reacted quickly to rectify his error.
The visitors stepped up the tempo in the second period and Jermaine Beckford tested Paul Jones, before Harley bagged a superb second from 25 yards to secure a priceless win.