Nikica Jelavic capped an impressive start by the visitors with a superbly-taken header, only for Wayne Rooney to bag a vital leveller for the hosts shortly before the interval.
Danny Welbeck and Nani put the Reds two goals clear with brilliantly-executed strikes, only for Marouane Fellaini to reduce the arrears with a neat volley. Rooney then capped another fine move to seemingly put the game to bed, only for Everton to muster a grandstand finish.
Jelavic bagged his second after sloppy defending from the Reds, before Steven Pienaar restored parity from close-range after the visitors had been allowed to stroll through the hosts' stunned ranks.
Despite sustained pressure from United thereafter, insufficient time remained for the champions to find a winner, and the next outing, at second-placed Manchester City, looks increasingly pivotal.
Sir Alex Ferguson made just one change to the side which had eased past Aston Villa a week earlier, with Nani replacing Ashey Young, who dropped to the bench. The visitors, shorn of Leighton Baines, shunted Sylvain Distin to left-back in the most noteworthy of three alterations from the starting line-up beaten by Liverpool at Wembley.
Though the devastating nature of that FA Cupdefeat might have impacted on their outlook, Everton began in impressively fine fettle. Leon Osman forced a sharp stop from David De Gea, then flashed a shot across the Spaniard's