Goals from Tim Cahill and Marcus Bent, either side of a Robbie Fowler strike consolidated Everton's third place in the table and took their points tally beyond the total they reached last season.
The visitors ran Everton ragged for the first 20 minutes as a catalogue of schoolboy errors saw the Toffees continuously surrender possession.
But when Bent was brought down by former Toffee Richard Dunne, they were gifted a 20-yard free-kick to break the deadlock.
The set-piece was expertly delivered by Thomas Gravesen who curled the ball to Tim Cahill and the Australian buried the ball in the top corner of David James' goal.
The unusually quiet Goodison crowd erupted and Cahill wisely decided to keep his shirt on as he celebrated his third goal this season.
Evertonians almost had another reason to be cheerful minutes later when a Steve Watson shot nearly found the target - only some quick thinking from James saw it fail as he managed to edge it away with a fingertip lunge.
The home side's joy was short lived.
A stupid challenge by Cahill brought down Antoine Sibierski and gifted Nicolas Anelka a free-kick, minutes before half time. The Frenchman passed the ball to former Liverpool striker Robbie Fowler, who buried the ball in the Gwladys Street goal.
Fowler took great delight in scoring against his boyhood heroes and ran a full circuit of the pitch taunting Everton fans.
But his enthusiastic celebrations also earned him a yellow card for time-wasting from referee Phil Dowd.
City almost snatched a lead early in the second half from a Danny Mills strike, but some quick thinking from Everton's Nigel Martyn saw the ball tipped around the right-hand post to safety.
Evertonians felt aggrieved after they were denied a penalty as Bent was tripped on the goal line after 60 minutes, but the Toffees bounced back and snatched a second goal less than five minutes courtesy of Mills.
The City defender brought down Gary Naysmith to gift Everton a 30-yard free-kick, again taken by Gravesen. The Dane passed the ball to Bent and the hard-working striker landed the ball in the centre of the City goal.
The earlier Christmas cheer dried up as the two sides became increasingly bad-tempered.
Mills received a yellow card after a two-footed tackle on Gravesen left the Toffees midfielder howling in pain.
And Gravesen was also yellow-carded when he clashed with Dowd after complaining that Mills should have been sent off.
Tempers finally boiled over when City substitute Christian Negouai was sent off less than five minutes after he came onto the pitch.
The defender's horrific two-footed tackle earned him a straight red card and almost sparked a mass brawl among the players.
The Toffees unbeaten run is now seven games and they face the prospect of going into the New Year in their best-ever Premiership position.