The Toffees were quickly out of the traps to take a second-minute lead through Chester-born striker George Waring but after a fairly even first quarter of the match, it was all about the Reds and how many chances Paul McGuinness' players could convert.
In the end, only Jack Rudge managed to find the net for the visitors, planting home a bouncing ball from close range in the 65th minute. But if the spectators braving the wet conditions expected the Reds to go on and win the match, they would finish up with a surprise.
Spurned opportunities by United and an inspired performance by the Everton goalkeeper locked the scores at 1-1 - not even the double introduction of substitute strikers Jack Barmby and James Wilson could force the issue in the Reds' favour.
The outcome left all those present to ponder how a second consecutive win had not been chalked up on the back of last weekend's 2-1 victory over Bolton.
United: Sutherland; Weir, Grimshaw, Dalley, Evans; Pearson, A. Pereira (Barmby, 79), Rudge (Wilson, 79), Rothwell, Daehli; Byrne. Subs not used: Gollini, Harrop, Ioannou.