Midfielder James McCarthy's first goal since May was followed in the second half by Romelu Lukaku's 17th of the campaign, one more than he managed in the whole of last season, before Newcastle captain Fabricio Coloccini was sent off and Ross Barkley made it 3-0 in added time.
It was a comfortable if not commanding performance but the Toffees were greatly assisted by Newcastle who, aside from one very early attack, rarely threatened and contributed significantly to their own downfall.
When you are on the sort of run Everton have been on, just one victory in their previous 12 top-flight games stretching back to mid-December which left them just three points above the relegation zone before kick-off, any slice of good fortune is warmly welcomed.
However, even they could not have imagined the assistance they were given by Magpies goalkeeper Tim Krul's horrendous misjudgement for the opening goal, although anyone who witnessed Newcastle's 5-0 drubbing at Manchester City recently could probably have predicted their second-half surrender.
Despite decent results in the Europa League, having beaten Dynamo Kiev 2-1 on Thursday, confidence remains fragile, especially at Goodison where a demanding crowd have been quick to get on the team's back in recent weeks, and that has had the effect of making players more ponderous in their passing.
While manager Roberto Martinez remains welded to his possession principles there is no doubt his side have recently become more direct than they have in the past, which in itself makes sense as it plays to the strengths of Lukaku.
The Belgium striker showed against Kiev how his power on the ball can pay dividends and his ability to hold up play was crucial in the opening goal.
Phil Jagielka drilled a 50-yard pass straight through a vacant Newcastle midfield all the way to Lukaku, playing right up against Coloccini, and he held it up just long enough for McCarthy to charge on to.
The Republic of Ireland midfielder still had some work to do but was assisted greatly by Krul who, despite having full view of the shot, embarrassingly dived the wrong way and watched as the ball went in past his outstretched feet.
It was the injury-troubled midfielder's first Everton goal at Goodison and only the second of his Toffees career.
McCarthy had earlier contributed to a potentially pivotal moment when he, with the help of a flailing elbow, kept out Mike Williamson's shot after goalkeeper Tim Howard had clawed away Gabriel Obertan's effort.
Aside from a Ryan Taylor free-kick flying just over early in the second half, the visitors offered little else.
Everton were making all the running and their best other chance on the stroke of half-time saw Antolin Alcaraz's downward header turned goalwards by Arouna Kone, on his first league start since New Year's Day, only to be hacked off the line by Taylor.
On-loan Tottenham winger Aaron Lennon, who had earned more praise for his defensive shift in the first half, started to find more space to run into after the break but he was actually heading away from goal when Yoan Gouffran fouled him inside the area.
Despite number-one taker Leighton Baines, making his 400th career appearance after returning from a five-match injury absence, being on the pitch Lukaku stepped up to dispatch the penalty - his fifth goal in six league appearances against Newcastle.
If that needless foul was not bad enough Coloccini's lunge on Lennon compounded their miserable afternoon.
After a week of debate about players trying to influence referees Darron Gibson, Leon Osman and McCarthy were all quick to point out to Martin Atkinson how poor a challenge it was but it was fairly obvious to all concerned it deserved a red card and Atkinson had no hesitation in sending off the Newcastle captain.
Osman forced a low save from Krul and then substitute Barkley, who replaced Lukaku, had a shot cleared off the line by Taylor.
Howard had to react smartly to deny Moussa Sissoko and Alcaraz blocked Remy Cabella's driving run but Everton's victory was never in doubt and Barkley emphasised that by rounding Krul with the last kick of the game.
Source : PA
Source: PA