Two Premier League victories, a Carling Cup win and a UEFA Cup success has been Everton’s response to losing the Merseyside derby last month in controversial fashion to Liverpool.

They looked well on the way to victory after Ayegbeni Yakubu put them ahead at the break, the one chance the Nigerian took when he could easily have had a first-half hat-trick.

Everton’s wastefulness continued after the interval, and they invited Birmingham back into the game. Olivier Kapo took full advantage to grab his fifth goal of the season.

The home side were deflated but in injury-time Lee Carsley, with a rising shot from 20 yards, and James Vaughan, after being sent clear, finally made sure the points ended up at Goodison Park.

Everton had Mikel Arteta back in their midfield after recovering from a calf strain, while Phil Neville also returned after suspension.

Birmingham restored Johan Djourou to defence after a two-match absence with a hamstring strain, while Wilson Palacios, whose 15-year-old brother was kidnapped last week back home in Honduras, was left out of the squad.

And Birmingham found themselves pinned back by Everton’s aerial attack from the off. Corners and free-kicks rained down on their defence, and they looked bemused by the onslaught.

Such was the disarray in the visitors’ defence, Everton almost scored after eight minutes through Yakubu, and he put the Merseysiders ahead two minutes later.

The first effort came after a strong Alan Stubbs run, followed by a Leon Osman cross that saw Yakubu’s effort deflected wide.

After 10 minutes, though, the big Nigerian was left embarrassingly unmarked as he strolled into the six-yard box to clip home Steven Pienaar’s cross, Arteta’s neat pass having opened up Birmingham’s defence.

Birmingham did pull themselves together eventually, and Kapo forced his way into the box to see a low shot palmed away by Tim Howard.

Then Everton lost Stubbs after 22 minutes, the veteran defender having apparently picked up an injury, and he was replaced by Phil Jagielka in the centre of defence.

Yakubu almost struck again after an error by Fabrice Muamba almost presented him with a second on 25 minutes. The £11.25million record signing intercepted a poor pass and surged into the box, only for Maik Taylor to block his attempted chip.

Birmingham were asleep again when Arteta got to the line a minute later and presented Lee Carsley with a 12-yard effort that Taylor gratefully held.

The chances kept coming and Yakubu chested the ball down to Tim Cahill, 30 yards out, and the Australian lashed a low drive inches wide of a post.

Yakubu continued the second half in a similar vein to the first when an Arteta free-kick into the box gave the striker the chance to send an angled drive across goal and just wide of the far post.

Cahill was next into the act, meeting a Neville cross with a firm downward header, again straight into Taylor’s hands.

Then Birmingham opted for a second striker to assist Cameron Jerome and sent on Garry O’Connor for Sebastian Larsson.

But Osman and Cahill both frittered away chances after a poor Taylor clearance, and regardless of how much Everton had been on top, their lead was precarious and Birmingham still had hope, even if they lacked direction in their play.

Everton paid for their wastefulness when Birmingham grabbed an equaliser with 11 minutes left. The visitors had sent on Gary McSheffrey and Mikael Forssell for Mehdi Nafti and Daniel de Ridder, encouraged by the fact that they were still in contention.

The goal came from a McSheffrey corner, met firmly by the head of Kapo, with his effort powering past Howard from six yards.

Everton’s response was to send on a second striker of their own, James Vaughan, for Osman before the restart. Vaughan almost grabbed a goal a minute later when his close-range effort from Pienaar’s cross was deflected wide.

Next on for Everton was Thomas Gravesen for Pienaar, and tempers began to fray after Kapo did not return the ball to the hosts quickly after Cahill had kicked the ball out to allow the injured McSheffrey medical attention.

But the atmosphere changed two minutes into injury-time when Carsley lashed the ball home 20 yards after Birmingham failed to clear a long throw.

A minute later it was all over when Carsley’s header sent Birmingham-born Vaughan clear to stab home the third.