Tim Howard let one slip by early on in the entertaining matchup between two teams pretty much just playing out their schedule.
Although the game was effectively a dead rubber for two sides who have little more to play for than the pride of a higher league position, it was far from a boring end of season encounter.
The match started brightly for both sides with a John Heitinga shot over the bar after good work by Leon Osman being followed closely by Peter Odemwingie hitting the side netting from six yards.
Such was the end to end nature of the first 15 minutes alone, the early goal that came was inevitable.
A ball over the top by Chris Brunt troubled Sylvain Distin who lost out on the ensuing physical battle to Odemwingie, leaving the Nigerian international in enough space to play it across to an unmarked Youssouf Mulumbu who passed home from six yards.
Everton almost hit back straight away minutes later as goalscorer Mulumbu was easily dispossessed by Phil Neville, the Everton captain fed Victor Anichebe to shoot straight at Scott Carson when he should have perhaps done better.
Everton continued its attempts to restore parity as Heitinga shaved the post with a header from a Tony Hibbert cross however, the more it opened up, the more West Brom looked a threat on the counter.
Another headed chance, this time for Odemwingie, who latched on to a flick on from a long throw in, was saved well down to his left by Tim Howard as an entertaining first half came to a close.
The second half resumed in similar fashion to the first. Leon Osman found acres of space in the West Brom box but miscued his half volley over the bar only minutes after the restart.
More good work from the lively Odemwingie almost created another goal at the other end as his teasing ball across the box was almost met by Simon Cox.
Without a goal forthcoming, Everton manager David Moyes soon looked to the bench for inspiration, as he brought on playmaker Diniyar Bilyadetinov in place of Phil Neville.
He was almost rewarded immediately as the Russian put a difficult effort over the bar shortly after his introduction. However, his contribution was about to end there.
The ball broke loose from a touch by Baggies midfielder James Morrison and the Everton player was rash and late in his attempt to retrieve it. Referee Anthony Taylor was left with little choice but to brandish a red card for what was a poor challenge.
The game as a contest effectively ended with the card and Roy Hodgson's side remained solid against 10 men to seal only its second clean sheet this season.