Conor McAleny and Yakubu scored Everton's goals in the 73rd and 75th minutes respectively to salvage Everton a point after efforts from West Brom's James Hurst and Saido Berahino had left the visitors 2-0 down.
Goalscorer Yakubu and fellow Nigerian Joseph Yobo were the most experienced names on the Everton teamsheet, and both played the full game in the behind-closed-doors fixture.
In the opening exchanges both James Wallace and Conor McAleny had efforts saved, but the Blues fell behind on 38 minutes to a James Hurst volley.
Despite suffering that setback Everton continued to attack and further chances fell to Yakubu and Femi Orenuga, whilst Yobo went close from a free-kick.
Youngster Berahino doubled the Baggies' advantage with a 68th minute tap-in, but Everton again responded well and were rewarded shortly afterwards.
A left-wing cross from Jake Bidwell was headed home by McAleny and just two minutes later the Blues were level as Yakubu's neat finish rescued a deserved point.
West Bromwich Albion: Fulop; Jones, McAuley, Ibanez (Downing 45), Mattock (Gayle 72); Hurst (Edge 85), Thorne, Mantom, O'Neil; Sawyers, Berahino. Subs not used: Daniels, Goldsmith.
Everton: Davies; Browning, Yobo, Mustafi, Bidwell; Orenuga, Wallace, Baxter, Forshaw; McAleny, Yakubu. Subs not used: Roberts, Duffy, Nsiala, Forrester, Higgins.