Joe Cole opened the scoring inside the first four minutes for the hosts, only for Anelka to return to haunt former manager Sam Allardyce - who signed the Frenchman for Bolton Wanderers back in 2006 - with a brace that put West Brom in command.
Anelka's first goals for the Midlands club proved not to be enough to secure the points as the hosts launched a second-half fightback, substitute Modibo Maiga restoring parity as Ben Foster allowed the forward's tame effort to creep into the net and Kevin Nolan pouncing for his first goal since the opening day of the campaign.
But West Brom refused to lie down and secured a share of the spoils after 69 minutes, Saido Berahino's fine individual effort ensuring West Ham remain in the relegation zone, although the visitors could not find a late winner and are now nine without a league triumph.
Jussi Jaaskelainen returned to West Ham's XI in place of Adrian, while Berahino and Anelka led the line for West Brom in six changes made by interim head coach Keith Downing.
The visitors went close early on when Chris Brunt volleyed into the side-netting from James Morrison's cross.
However, they fell behind moments later, Joe Cole slotting home with a cool finish following neat link-up play with Kevin Nolan.
James Tomkins was forced off with a groin injury, and replaced by Guy Demel, and the switch seemed to give West Brom the initiative in possession as they dominated play.
However, it was the hosts who continued to create the better opportunities, Carlton Cole heading well over from a Matt Jarvis corner before Demel shot wide from point-blank range.
Mark Noble spurned another chance for West Ham as he curled a free-kick off target, and Allardyce's men were made to pay for their profligacy just five minutes before the interval when Anelka converted from Brunt's throughball to net for his sixth different Premier League club.
And Anelka capitalised on poor defending from West Ham in first-half injury time to score his second after the hosts had failed to clear Brunt's corner.
Maiga was brought on for Carlton Cole at the break and made an instant impact, testing the reflexes of Foster before finding the net in the 65th minute with a curling shot that crept under the England goalkeeper's body.
The turnaround looked to have been completed two minutes later when Nolan bundled the ball home for a Maiga knock-down to score only his second goal of the campaign.
But there was to be yet another twist in the tale, which came courtesy of England Under-21 international Berahino, who teased the West Ham defence before firing in off the post.
West Brom finished the contest the stronger of the two sides, Berahino hit the woodwork with a free-kick, but the visitors could not find a dramatic late winner.
