Daniel Sturridge opened the scoring midway through the first half with Liverpool's first shot on target, guiding home a Luis Suarez cross from close range after intelligent play between Philippe Coutinho and Raheem Sterling.
Suarez then saw a free-kick curl inches away from the post with Ben Foster rooted to the spot before Zoltan Gera fired wide at the other end in a relatively low-key opening 45 minutes.
Pepe Mel's side made a lively start to the second half, with Gareth McAuley drawing a fine one-handed save from Simon Mignolet.
Suarez came close to doubling Liverpool's lead after getting the better of Diego Lugano and audaciously beating McAuley, but Foster was on hand to deny the Uruguayan.
The visitors looked to be on course for their second victory of the week but Toure's loose ball across goal was seized upon by Anichebe who lashed past Mignolet into the bottom corner to secure a valuable point.
A draw gave more ammunition to the critics who felt Liverpool should have strengthened in the transfer window to enhance their bid to regain Champions League football.
But it was not the absence of Yevhen Konoplyanka, whose move broke down on deadline day that cost Liverpool the points, but a lack of resources at the back.
Essentially, what Liverpool really need is to keep Suarez and Sturridge fit and firing, and while at least one of them kept up that end of the bargain there were failings elsewhere.
During the midweek Merseyside derby victory, Suarez and Sturridge were falling out over who should pass to whom but there was no such disagreement here, with the in-form strikers on the same wavelength.
The continually-improving Sterling was released through the inside-right channel and held the ball up long enough for Suarez to go round the outside of him to receive the pass.
Suarez's movement to generate space for the cross was brilliant and he picked out Sturridge at the far post for the England international to convert. He has now scored in 15 of 19 games this season - but even he paused before celebrating as he was not entirely sure whether he was onside.
There was little else in the way of chances in the first half with Suarez failing to properly plant his head on a Coutinho corner and then being denied the decisive touch on Aly Cissokho's cross by Jonas Olsson, who injured himself in the process and was replaced by Lugano.
West Brom's first-half efforts amounted to Youssouf Mulumbu's drive, blocked by Steven Gerrard although it appeared to be going wide, and Gera's shot which fizzed across Mignolet and wide of the far post.
The home side came out with greater intent after the break and a period of early pressure resulted in Mignolet saving well from McAuley's powerful header.
It seemed apparent 1-0 would not be enough for Liverpool to hang on to and Suarez should have made it more comfortable when he brought down Toure's long ball, sidestepped compatriot Lugano, cut back inside but was denied by the outstretched leg of Foster.
Mignolet made another good save, this time from Chris Brunt's low free-kick on the edge of the penalty area, but was helpless to prevent the equaliser.
Brendan Rodgers wants his side to play out from the back but Toure, unlike Daniel Agger, is not comfortable on the ball and inexplicably passed straight to Anichebe 20 yards out and the former Everton striker made the Ivory Coast defender pay dearly for his mistake.
Liverpool's switch to three at the back following the introduction of Martin Kelly and Joe Allen saw Sturridge denied by a charging Foster with Toure heading over Gerrard's resulting corner.
It was to prove the last real chance as Liverpool did not carve out enough openings for their potent strikeforce to benefit.