The Blues are still without a Premiership home win this season and this was their fifth defeat at St. Andrew's.
Everton, meanwhile, are showing signs of playing themselves out of trouble and the win moved them off the bottom of the table.
Following their impressive display in holding Chelsea to a 1-1 draw in their previous game, they carved out a vital win thanks to Simon Davies' first goal of the season - a strike which left home goalkeeper Maik Taylor with egg on his face.
With so much at stake it was hardly surprising that neither team played with any real conviction in the early stages.
Nicky Butt, who had never been on a beaten side playing against Everton, and Damien Johnson worked hard in midfield to generate some spark but strike pair Emile Heskey and Mikael Forssell were both sadly off the pace.
Everton were very cautious in their early play but slowly dragged themselves into the match.
Tim Cahill was the inspiration and the Australian gave the visitors hope with a shot on the run which went just wide. The attempt sent out the message that Blues' defence could be penetrated.
In sharp contrast the hosts failed miserably to make any real impact as an attacking unit. Their only real attempt in the first half was a tame free-kick from Jermaine Pennant which was easily handled by Nigel Martyn.
Cahill then popped up with a diving header which Maik Taylor saved in fine style, but the Blues keeper was at fault when Everton took the lead in the 43rd minute, with only their third Premiership goal of the season.
Andy van der Meyde broke clear on the left and his pass into the middle found Davies, who hammered in a low shot which bounced just in front of and over the body of Taylor.
This was yet another body blow for Blues, who have hit their worst spell during Steve Bruce's four-year reign.
As usual, Blues found themselves chasing the game and this created a panic situation which did little to enhance their prospects.
They often left themselves exposed at the back where Martin Taylor's lack of pace was highlighted when James Beattie and Duncan Ferguson both went close to increasing Everton's advantage.
Only an alert Maik Taylor prevented Everton from scoring on each occasion.
The hosts, however, were out of luck in the 65th minute when teenager Neil Kilkenny, who had taken over from the experienced Butt in the first half, saw his low free-kick hit the post and bounce across the face of Everton's goal.
As Blues' disgruntled fans began to stream out of the ground substitute Walter Pandiani carelessly wasted a glorious chance to equalise when he scooped his effort from close range over the bar.