Albion's opening day of the season win was quickly forgotten after Everton came from behind to beat the Baggies 2-1 at The Hawthorns.
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It was the second successive comeback win by Everton at the Hawthorns.
A loss it might have been, but what will be of huge encouragement to Albion fans is the number of efforts on goal they had.
The game may have panned out very differently had Fletcher been more predatory when he was presented with a great chance early in the second half.
But Albion fell behind on the hour mark - and it was a goal that could have been easily avoided.
It all started when Olsson gave away a free-kick 40 yards out for bringing down Mirallas after a poor touch.
Foster pulled off a remarkable full-stretch save to deny Funes Mori's header from that free-kick, but he couldn't do anything about the corner.
Holgate's volley goalwards bounced up over Albion's defence and hit Barry in the face two yards out before finding the roof of the net. It was exactly the same position McAuley had scored from in the first half.
Ronald Koeman got his first Premier League victory as Everton manager as West Brom lost 2-1 at The Hawthorns in front of new owner Guochuan Lai.
Lai, who heads the Chinese investment group which at the beginning of this month completed its takeover of the club, saw his team make the perfect start to their home campaign as Gareth McAuley headed Albion into an early lead.
However, goals from Kevin Mirallas and Gareth Barry either side of half-time saw Koeman claim his first three-point haul as Toffees boss after drawing 1-1 at home to Tottenham on the opening day.
Lukaku started on the bench at The Hawthorns, having been sidelined with a foot injury, but his introduction in a tactical change towards the end of the first half swung the match in Everton’s favour after Gareth McAuley had headed Albion in front from a ninth-minute corner.
Everton had started with three at the back, four across the middle and a front line without a recognised striker. But after Koeman switched to a defensive four and introduced Lukaku as a target man they began to find penetration to go with their dominance of possession.
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