The Toffees have just one win in their last 13 matches in all competitions and could not end their slump at home to the Baggies despite dominating possession at Goodison Park
Despite Baines's impressive record from 12 yards, Mirallas took charge of proceedings after Joleon Lescott had handled - but put the ball wide before being substituted by Roberto Martinez at half-time.
The early withdrawal of Mirallas, in the wake of the Belgian seemingly over-ruling team orders by taking the penalty, is likely to prompt more questions over the future of a player apparently interesting the likes of Tottenham.
And the hosts' frustrations continued into the second half as West Brom - adopting a defensive approach that saw them fail to muster a shot on target - held firm in the face of persistent pressure to pick up another point in their bid for survival as the pressure surrounding Martinez continues to grow.
Everton are now winless in six Premier League outings and only four points above the relegation zone, while West Brom are a point worse off and remain unbeaten under head coach Tony Pulis, who has wasted little time in stamping his mark on his new club.
Martinez brought in Mirallas for the suspended Aiden McGeady and the forward had the game's first effort on target when his shot was gathered comfortably by Ben Foster. But while Everton dominated the early possession, they were unable to break down a deep West Brom backline.
The visitors made a rare foray forward 20 minutes in, but Andre Wisdom failed to muster an effort on goal after getting into the Everton area. Soon after, Mirallas again tested Foster - this time with a freekick - before Muhamed Besic saw a long-range strike deflect wide.
While Mirallas had been among the bright sparks for Everton in a relatively dour first half, he spurned the best chance to send his side in ahead at the break. After Lescott had clumsily handled in the area, Mirallas could only stroke the ball past Foster's right-hand post to add to Everton's misery.
It proved to be his final contribution of the game as he was replaced by Bryan Oviedo at the break - a decision that will only fuel rumours of a January exit.
Even a big-screen appearance from Hollywood legend Sylvester Stallone at the break could not add any stardust to proceedings, though Everton's dominance continued even without Mirallas. Pulis's men stood firm, though, with the Welshman replacing Saido Berahino with midfielder Graham Dorrans to further tighten up at the back.
Martinez threw Arouna Kone on for the impressive Besic, but the Ivorian failed to provide an elusive winner as Foster remained relatively untroubled.
While Baines forced a free-kick late on, the full-back’s delivery was poor and immediately cleared, and the Goodison Park faithful filed out to ponder when their ongoing malaise will end. They greeted the full-time whistle with boos as their side's slump extended to just one win in 13 matches in all competitions.