Blackburn Rovers picked up a deserved point at Everton thanks to David Goodwillie's equaliser, but remain in the Premier League's bottom three.
Tim Cahill gave Everton a controversial lead with Maroune Fellaini's handball in the build-up missed by the referee.
Rovers hit the post twice in the first half through Scott Dann and David Dunn and were generally the better team.
They levelled after Tim Howard's fumble saw Cahill crash a goal-line clearance off Goodwillie and into the net.
Draw was a fair result - Moyes
The result saw Blackburn temporarily move out of the bottom three, but Bolton's 3-1 victory over Liverpool later in the day saw them slip back into the relegation places.
Nonetheless manager Steve Kean would have been highly encouraged by what was an excellent performance from his team.
The opening periods of the game were entertaining with both sides going close. Victor Anichebe made a mess of a volley at one end for Everton and Howard used his feet to save well from Dunn, following David Hoilett's fine run.
Blackburn looked the most likely to break the deadlock, though, with Dunn in lively form while Dann saw his looping far-post head bounce back off the post.
Did you know?
Tim Cahill's last goal for Everton was on 20 December, 2010.
But it was Everton who took the lead and, having gone close moments earlier through Phillip Neville, who was celebrating his 35th birthday, they went ahead in controversial circumstances.
Cahill scored it, his first goal in 34 games, tapping in from close range. However Fellaini should have been penalised by Mark Halsey in the build up for a handball as he palmed the ball into the Australian's path.
Blackburn refused to feel sorry for themselves and went in search of an equaliser. Dunn crashed a shot off the post from just inside the box after Goodwillie's cross was deflected into his path.
Blackburn performance pleases Kean
Cahill had a late header on the stroke of half time which was saved by Paul Robinson but it was the closest they would go for a while.
Blackburn pressed hard in the second half, starting it brightly but struggled to create a clear cut opportunity - missing suspended striker Yakubu's power up front. Radosav Petrovic tried his luck from 30 yards with his shot a foot wide of Howard's post.
Everton introduced Royston Drenthe for Louis Saha while Mauro Formica came on for Dunn as Steve Kean tried another option.
Drenthe's first real contribution was to fire a fierce ball across the face of the goal but no Everton player could keep up with the speedy Dutchman.
And Blackburn got the equaliser their play deserved in fortuitous circumstances.
Morten Gamst Pedersen's free kick into the box slipped through the hands of Howard and as Cahill went to clear the ball off the line it crashed against Goodwillie and went into the back of the net.
It meant Blackburn kept their record of scoring in every league game away from home.
Did you know?
Blackburn have failed to keep a clean sheet this season.
Everton went close to retaking the lead late on with Shane Duffy unlucky to see his close-range header come back off the crossbar while at the other end Formica's chip was just wide for Blackburn
And then in the last minute Everton again came close with a combination of fine keeping and brave defending keeping them at bay. First Fellaini saw his header cleared off the line and then Denis Stracqualursi's subsequent shot was well kept out by Robinson.
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