It meant that of the Merseyside clubs it was Everton that got the better of the weekend's results, and they trail fourth-placed Liverpool by just two points.
Anichebe even received encouragement from the Everton camp, with club masseur Jimmy Comer sending him a text message that fired up the 25-year-old as he prepared to come off the bench.
Substitute Anichebe seized on a sloppy crossfield pass from Kolo Toure and finished well into the bottom left corner from a central position, drawing West Brom level after Daniel Sturridge had tapped Liverpool ahead in the first half at the Hawthorns.
"It's always nice to score," Anichebe told Sky Sports 1.
"I was sitting on the side itching to get on. I got a text from one of Everton's masseurs, Jimmy Comer, saying 'Help us do the Reds today'.
"I felt I was going to come on and help the team, even though I wasn't playing from the start.
"But the team, they did ever so well. Saido (Berahino) and (Matej) Vydra did well to work the Liverpool defence. I just came on and I helped the team."
Anichebe anticipated well to intercept and take his chance, saying: "Sometimes in the past I might have switched off but today I was ready, especially against Liverpool. I was there and I finished it."
Liverpool manager Brendan Rodgers promised Toure would not be taken to task over his mistake.
"I've never criticised my players for trying to play football," Rodgers said on Sky Sports News.
"Kolo probably shouldn't have received the ball under pressure, and a pass can be misplaced.
"We look to build our game from behind and that has won us many games this season, our ability to construct the game from behind.
"Sometimes it will cost you. Today was unfortunately one of those days.
"Kolo Toure has been brilliant for me, a real leader and an outstanding professional and unfortunately it was that mistake, but there's no blame on him."
Rodgers also played down worry over dropping points.
"Obviously we're disappointed not to have taken all three points but it's another point furthermore for us in terms of where we want to go," he said.