Jermain Defoe scored his 13th goal of the season and Michael Dawson his second in two Premier League games, but two late goals in a dramatic finish including a missed penalty saw Everton leave the field in a happier frame of mind at Goodison Park.
Two goals up and good value for the lead, the team did not press home their advantage and a squandered penalty by Defoe in the fifth minute of injury time only increased the feeling that this was two points dropped from a clear winning position.
Harry Redknapp reverted to the side that started against Aston Villa last weekend and it was Heurelho Gomes who was first called into action when he reacted with a smart save when an attempt by Jo came off the knee of Vedran Corluka and travelled goalwards.
After some swift countering involving Jermain Defoe and Aaron Lennon, Jack Rodwell was more purposeful with his surge towards goal, with Gomes again called into action.
Peter Crouch worked himself into a clear goalscoring position on seven minutes when a sortie by Lennon provided the supply line, but the England striker could not keep his shot down and a collective sigh of relief went around Goodison Park. There was another moments later when Defoe worked himself a yard of space following a Tom Huddlestone throughball and only the feet of Tim Howard prevented an opener.
Everton were forced into a change with just 15 minutes going, Joseph Yobo unable to carry on and was replaced by full-back Seamus Coleman with Tony Hibbert moving inside to central defence.
Michael Dawson was forced into an interception when Diniyar Bilyaletdinov took advantage of a slip by Benoit Assou-Ekotto, with Gomes doing well to punch clear from the resulting corner, while Howard nearly fumbled a tame effort from Crouch at the other end.
Rodwell then chipped in the direction of Jo, the Brazilian proceeding spin in the area before dispatching a low drive that zipped across the face of goal. Coleman and Pienaar combined to present Jo with another chance, this time from six yards out, but thankfully his effort squirted wide under pressure.
Some of the early fluency was ebbing away as Everton were establishing a presence in the game and becoming a more effective force. Gomes, however, was showing a clean pair of hands and clutched a Leighton Baines free-kick from just outside the area with ease.
Defoe shot just wide when a goal looked in the offing on 32 minutes after clever work from Niko Kranjcar. It took a flashpoint to really bring the home crowd to life, one that resulted in Assou-Ekotto and Marouane Fellaini seeing yellow.
A Howard advance off his line denied a determined Defoe a few minutes before the break, while in stoppage time the goalkeeper allowed a teasing Lennon cross to bounce off his chest and the American was fortunate that it fell to one of his own players.
Gareth Bale was introduced after the break in place of the booked Assou-Ekotto, with the early impact nearly made by Defoe, who was played through on goal by Huddlestone. His effort did not carry any conviction.
You could not say that about his next in the 47th minute when a Lennon cross to the near post was seized upon and directed past the helpless Howard to open the scoring with his 12th Premier League strike of the season.
Crouch nearly added to the tally when he pounced on defensive indecision and it was only the fingertips of Howard that prevented a doubling of the advantage - although the referee did not see fit to award a corner.
Everton responded by building up a degree of momentum, but Captain Dawson made it two goals in two league games on 59 minutes. Kranjcar swung in inviting corner and 'Daws' plunged himself forward and connected with a thumping header that gave Howard no chance.
David Moyes went for broke by bringing on Yakubu and Louis Saha, which prompted a flurry of high balls and second ball pressure, while Bale came close to relieving a little of the pressure when his free-kick flew just wide of the top corner.
Crouch again could have added his name to the scorers with 13 minutes left after being played in by Kranjcar to the left of the area, but he screwed his low shot wide of the far post.
Saha managed to reduce the deficit in the next move after a Coleman sprint down the flank resulted in a low cross being put towards the near post. Saha was later not far away with an overhead kick as some less than clinical finishing looked like it might prove costly. A game that could have been sewn up was now shredding the nerves.
Fears were proved well founded when, with a few minutes left on the clock, the home side levelled. Coleman crossed from the right, Baines drilled back in from the left and the head of Tim Cahill was responsible for steering into the net.
More drama was to come. Palacios was clattered in the area by Hibbert in stoppage time and referee Mr Marriner pointed to the penalty spot. Wilson required lengthy treatment and ended up being stretchered off and when the kick was eventually taken Howard saved Defoe's kick with his feet in the centre of the goal.
It was a point won, but the late smash and grab made it feel like a loss in the end.