Dyche proud of his Everton players who are 'giving everything'
Dwight McNeil, Abdoulaye Doucoure and Beto scored the goals as the Toffees' fine form continued despite the blow of being hit by the toughest sporting sanction dished out in Premier League history for breaches of financial rules.
Newcastle were made to pay for two uncharacteristic errors by England international Kieran Trippier as fatigue hit the injury-ravaged Magpies in the closing stages.
McNeil pounced to smash into the top corner 11 minutes from time before Doucoure secured a fifth win in seven games for Everton.
Substitute Beto rounded off victory with his first Premier League goal in stoppage time.
Victory lifts Everton one point clear of the bottom three and they would be in the top half but for the points penalty.
"This season, apart from the obvious with the 10 points, we’ve been in terrific form," said Everton boss Sean Dyche.
The Everton support have been galvanised by the perceived injustice of the severity of the points deduction and for once a raucous atmosphere was met with some reward at Goodison.
Everton's only two home Premier League wins since March had both come against Bournemouth.
"We’ve got some talent but you’ve got to give everything and there is that connection with the fans because they are seeing a group of people giving everything."
Newcastle's away day blues
Newcastle have swept aside Paris Saint-Germain, Arsenal, Chelsea and Manchester United at home this season.
But Eddie Howe's men have won just once away from home all season in the Premier League.
Newcastle remain seventh, four points off the top four.
An injury crisis has meant Trippier has played virtually every minute of their Premier League and Champions League campaign so far.
However, Howe said his side cannot allow tiredness to become an excuse with a packed schedule still to come before the end of the year.
Newcastle face AC Milan in a do-or-die Champions League clash next week to reach the last 16 and face Chelsea in the quarter-finals of the League Cup, on top of their Premier League commitments in the busy festive period.
"We can’t look at it that way because we have more games to go," said Howe.
"It's a combination of a lot of things. When you don’t perform you have to take ownership of it as that’s the best way to improve. Certainly there is a lot to reflect on."
Everton's upturn in fortunes would have been even better but for a consistent failure to make the most of their chances at Goodison.
Dyche was left to rue his side's profligacy in front of a goal as a positive first-half performance went without reward.
Dominic Calvert-Lewin then somehow blazed over with the goal gaping from close range after Newcastle failed to clear a free-kick into the box.
Alexander Isak headed the best of Newcastle's openings wide in the first half when unmarked at the back post.
Anthony Gordon endured a frosty reception on his return to Goodison, but even the in-form winger was wasteful in front of goal.
Gordon fired straight at Jordan Pickford after robbing James Tarkowski on the edge of the box and then failed to keep his composure when blazing well off target from Isak's through ball.
But the game swung in the closing stages on Trippier's errors.
The right-back coughed up possession to allow McNeil to surge forward and smash a perfect strike past stand-in goalkeeper Martin Dubravka.
Moments later, Trippier was again at fault as this time he gifted Jack Harrison possession.
McNeil failed to make contact with Harrison's cross, but the ball fell kindly to Doucoure to slot home.
Beto rounded off a perfect night for Everton late on as he showed impressive strength and produced a cool finish through Dubravka's legs for his first goal at Goodison.
