David Moyes was hoping his side could turn recent good performances into maximum points after the frustrating draw with Middlesbrough on Boxing Day.
Phil Neville, Andy van der Meyde and Nuno Valente returned to the starting eleven in an attacking 4-4-2 formation with impressive youngster Victor Anichebe keeping his place alongside Andy Johnson.
Magpies boss Glenn Roeder was looking for only his third win away from home this season and decided to drop Antoine Sibierski, Pavel Srnicek and David Edgar to the bench after the defeat to Bolton four days ago.
Everton made their now customary bright start, and it was no surprise when they went ahead in the ninth minute after a Mikel Arteta cross caused confusion in the Newcastle area and allowed Anichebe to prod home from close range.
Minutes later Arteta could have made it two but failed to latch on to Neville's wonderful lofted ball after Obafemi Martins lost possession after a great run.
Valente made a last-gasp clearance on 18 minutes after good work by James Milner, Martins and Paul Huntington. Emre almost levelled for the Magpies a minute later but hit a good effort into Tim Howard's side-netting.
The Turkish international received a caution for a harsh challenge on Joseph Yobo shortly afterwards.
Newcastle were beginning to show their frustration as they lost their shape and discipline and Everton began to run riot with Johnson coming within a whisker of a second goal for the Toffees.
Howard though had to make a smart stop to his right after a Huntington cross found the head of Martins.
Kieron Dyer won a penalty after being brought down by Leon Osman just before half-time but there was more consternation as a petulant Emre tried his best to start a brawl with a number of players.
In truth the Turk should have walked but the referee missed the flashpoint. In any case Emre's behaviour only served to contribute to his team-mate Martin missing his spot kick.
After the Magpies' woeful first-half display it would have been a goal they little deserved.
Newcastle made a marked improvement after the break and had Everton on the back foot as the Toffees defended too deeply and needlessly invited pressure onto the back four.
However, Anichebe scored his second goal on 56 minutes to settle Everton nerves. Arteta's corner found Johnson's head and Anichebe flicked the ball on to the underside of the crossbar before finding the net at the second time of asking.
Van der Meyde could have made it three minutes later but failed to connect with a stunning cross from Valente. Scott Parker then had the ball in the net for Newcastle but was flagged offside.
Neville did make it 3-0 on the hour mark as he scored his first Premiership goal for Everton after he volleyed home Arteta's free-kick which Shay Given could only get his fingertips to as it sailed over his head and into the net.
Yobo cleared over his own goal after great work by Huntington again who seemed to be fighting a one man battle at times.
Johnson and Anichebe made way for James McFadden and James Beattie on 71 minutes as the Toffees threatened to rout an increasingly inept Newcastle side.
Parker was booked for scything down sub Simon Davies with five minutes to go to round off a dreadful afternoon for Roeder's men.