Oumar Niasse stepped off the bench to rescue a point for Everton but the game was overshadowed by a serious injury to midfielder James McCarthy.
The Republic of Ireland international suffered a suspected double leg fracture in a 61st-minute challenge with Salomón Rondón and had to be taken off on a stretcher.
At that point, Everton were trailing to Jay Rodriguez’s early opener but Niasse swept home from debutant Theo Walcott’s nod down 57 seconds after entering the fray to level with 20 minutes remaining.
The headline team news was the inclusion of Walcott, who made his Blues bow three days after completing his transfer from Arsenal. There was also a first Goodison appearance for the Club’s other January recruit, Cenk Tosun. Back came Ashley Williams, Morgan Schneiderlin and Nikola Vlasic as Allardyce made four changes to the side that was beaten at Wembley by Tottenham Hotspur a week earlier.
Before kick-off, the Goodison crowd, both home and away fans, paid tribute and acknowledged the legacy left behind by former Baggies striker Cyrille Regis, a minute’s applause recognising the 59-year-old who sadly passed away on Monday.
The Baggies had earned their first victory in 20 matches the week before against Brighton & Hove Albion and they were the quickest out of the blocks here.
On seven minutes, Rodriguez escaped, ran through the middle and converted into the bottom corner.
The warning signs had been there a minute earlier, however, when Polish international Grzegorz Krychowiak had fired narrowly over from a well-worked move.
It took Everton a while to respond to the early setback and had Schneiderlin managed a little more headed contact on Gylfi Sigurdsson’s 18th-minute free-kick then the Blues could have been back level.
Likewise, West Brom were inches away from going two goals up when Chris Brunt’s inswinging cross from the right beat everyone inside the box and nearly snuck inside the far post, with Jordan Pickford scrambling across his six-yard area.
It proved to be a fairly unremarkable first half. Sigurdsson thrashed a shot goalwards only to see it charged down, and right-back Jonjoe Kenny cut inside and forced Ben Foster into a decent stop, but other than that Everton were unable to conjure up the creativity to break down a disciplined Baggies defence.
There was another nervy moment for the hosts on the stroke of the interval when, from a left-sided corner, Rondon powered a header just over the top.
Allardyce’s response at the break was to swap Vlasic for Yannick Bolasie, who took up an attacking position alongside Tosun and Walcott.
Twelve minutes into the second half, McCarthy suffered a serious injury when attempting to tackle Rondon.
The Republic of Ireland international raced back to make a goal-saving intervention inside his own penalty area and was hurt in the contact with the West Brom striker. Rondon was visible upset following the incident and needed to be consoled by his manager Alan Pardew and teammates.
Wayne Rooney took the place of McCarthy and Niasse was introduced not long after for Tosun, who lasted 68 minutes on his home debut.
Both were involved in the Blues’ equaliser, scored by the Senegal forward with his first touch.
Rooney played a diagonal from the left, Walcott nodded it back across the six-yard box and Niasse volleyed in instinctively at the near stick. A great finish from the striker - his first goal since the middle of November.
Phillips spurned a chance to put the visitors back ahead following a low save from Pickford as both sides pressed and probed in a lively end to the contest.
Walcott very nearly had a debut goal to his name a quarter of an hour from the end, only to see his crisp volley turned away by Foster.
The Baggies stopper later kept out Bolasie’s low drive, while Pickford was also needed to make vital late stops from Phillips and Rondon.
Everton now have 10 days without a game before returning to Premier League action when Leicester City visit Goodison Park.