Everton's successful Under-23 coach David Unsworth has been in temporary charge since Koeman's departure and had some support to be appointed full-time but has won just won and lost five of his seven games at the helm.
Of the back four only Jonjoe Kenny remained, with Ashley Williams, Cuco Martina, and Mason Holgate coming in for the injured trio of Michael Keane, Phil Jagielka and Leighton Baines, while Tom Davies replaced Morgan Schneiderlin in holding midfield and Wayne Rooney returned to the lineup at the expense of Kevin Mirallas.
A returning David Moyes would have been hoping his side could take the momentum they had gained from their home draw with Leicester City last Friday with them to Merseyside, however, the Hammers fell well short and were considerably off the pace. My best teams play on the front foot and try and put teams under pressure, sometimes get a bloody nose in doing that, and that's what I'll deliver here at West Brom.
Though that goal failed to open the game, Everton doubled their lead ten minutes later.
Allardyce overtakes Real Madrid's double Champions League victor Zinedine Zidane, Atletico Madrid's Diego Simeone, Juventus manager Max Allegri and PSG chief Unai Emery.
West Ham were poor throughout the match, registering their first shot at Jordan Pickford's goal in the 52 minute, although they were given a lifeline when they were awarded their own spot kick. "To make it my first hat-trick for Everton, I'm delighted".
Tony Pulis was sacked on November 20 following 10 Premier League games without a win, despite having never been relegated from the top flight in his 10 seasons in charge in the division.
Wayne Rooney scored a wonder goal from his own half on Wednesday.