Marouane Fellaini headed over in a poor first half before Steven Pienaar's shot was well saved as Everton pressed.
On the half-hour mark Ladislav Onofrej had a penalty shout correctly rejected after he was cleanly challenged by Marouane Fellaini.
Marouane Fellaini headed home the opener in the 42nd minute before Steven Pienaar doubled the lead in the 59th minute.
Marouane Fellaini gave Everton the lead when he slotted in Leighton Baines' cross before Tim Cahill headed in Steven Pienaar's corner.
The Toffees, without their top scorer Tim Cahill, relied on Saha, Rodwell, Marouane Fellaini and Diniyar Bilyaletdinov to provide the bullets.
He had played a starring role, Marouane Fellaini had been outstanding and Tim Cahill had put in his best performance in weeks.
When Aimar played a short ball to Di Maria, Marouane Fellaini dawdled in defence and another smart cross proved easy pickings for Cardozo.
Pompey's Aruna Dindane saw his strike saved by Everton goalkeeper Tim Howard before Marouane Fellaini's close-range header was kept out by James' foot.
Osman, Marouane Fellaini and Phil Neville got to grips with the midfield and allowed Everton to dominate possession and territory from the outset.
Boro led 1-0 at half-time through David Wheater's 44th-minute goal but Marouane Fellaini and Louis Saha scored to give Everton a showdown against Manchester United.
Yet the Toffees were made to pay a high price when the statuesque Marouane Fellaini catastrophically slipped outside his own penalty area in the seventh minute.
But it was not an advantage they were to hold for long, despite the efforts of the tenacious Marouane Fellaini, who did his best to repel the Gunners.
Louis Saha has been plagued by hamstring trouble which has restricted him to 14 matches this season, while midfielder Marouane Fellaini is playing with a cracked bone in his back.
The hosts went ahead with a thumping drive from Dmitri Likhtarovich but Marouane Fellaini drew Everton level from a Leighton Baines free-kick and Tim Cahill won it with 13 minutes remaining.
Paul Lambert's Villa had been 3-1 up against Everton at Goodison Park, before two goals from Marouane Fellaini -- the second in injury time -- rescued a point for the Toffees.
With three minutes left, Carroll rose into the London sky with big-bodied opponent Marouane Fellaini all over him, met Craig Bellamy's free kick and headed it past Everton goalkeeper Tim Howard.
The hosts, full of graft and bite, hit back immediately when Phil Neville lashed a low drive into Blues keeper Petr Cech's arms before Cahill and Marouane Fellaini had headed attempts on goal.
Joy at last week's 2-1 victory over Chelsea was dampened by dismay over the tea-time kick-off and the pre-match news that midfielder Marouane Fellaini requires an operation on his injured ankle and will be out for six months.
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