It was a fine sweeping move for Albion who retained possession well in midfield before Adam Lallana picked out Joel Veltman on the right flank.
Veltman took a touch and clipped a delightful ball into the box which found Albion's leading scorer Neal Maupay.
The French striker spotted a darting run from Mac Allister and his cushioned header was perfect for Mac Allister whose composed first time finish whistled under the body of the advancing Jordan Pickford.
It was the second Premier League goal of the season for the Argentina whose previous strike came on the opening day of the season at Burnley.
A header from Dan Burn put Albion 2-0 up against the Toffees and worse was to come for Everton when Dominic Calvert-Lewin mised a first half penalty after Enock Mwepu clattered into Anthony Gordon