Sam Allardyce said he is "baffled" by Everton's poor defending before he arrived at the club after securing a third clean sheet in four games at luckless Newcastle.
Wayne Rooney's solitary close-range goal was enough for the Toffees to win their first Premier League away game since January, and extended the hosts' winless streak to eight games.
Newcastle's miserable night was compounded deep into injury time when Jonjo Shelvey was sent off for an ugly lunge on Idrissa Gueye.
Rafa Benitez's struggling side hit the woodwork twice through Matt Ritchie and Mikel Merino before the break, but always had to be wary of the Merseysiders' Gylfi Sigurdsson-inspired counter-attacks.
Former Magpies manager Allardyce's new club now move level on points with ninth-placed Watford, but Benitez's men are just a point off the bottom three as takeover talks between owner Mike Ashley and a group led by businesswoman Amanda Staveley continue.
Everton had to weather a late flurry from the hosts who threatened through Christian Atsu and dominated possession in the closing stages but could not find a way past Jordan Pickford.
"Their determination and drive has given us the opportunity to win a game 1-0," said Allardyce. "I'm a little baffled at how Everton conceded so many goals before I got here.
"We're up to 22 points so we're pushing our way into the top half and it all comes from a good solid defensive base.
"The Christmas party is postponed. They won't be anything near enjoying themselves until after the cup on 5 January."
He has postponed the Christmas party while demanding "magic" in return from his players, and so far Allardcye is getting everything he wants at Everton.
There was no sign of sulking from his team on Tyneside, which already seems fitter and more focused than under previous manager Ronald Koeman, despite having a day less to recover than the hosts from the exertions of Sunday's Merseyside derby.
So far as magic goes, Sigurdsson and Rooney are certainly showing some burgeoning alchemy in their link-up play. The Iceland international had struggled for form in the first part of the season but has become increasingly influential since Allardyce's arrival, while Rooney has scored five.
Newcastle must dread facing the former Manchester United striker. He has now been involved in 23 goals in his 23 Premier League appearances against them (15 goals, 8 assists) - more than versus any other opponent.
At the back Ashley Williams, struggling badly for form until Allardyce's appointment, was in dominant mood, while defensive midfielder Gueye was full of endeavour.
Allardyce said he will "pay his players back" for postponing their festive celebrations if their Premier League upturn is intact by January.
At this rate, he'd better have deep pockets.
Newcastle can offer up some hard-luck stories from a night that saw them strike the woodwork twice, have more possession, crosses and shots than the visitors.
But hard-luck tales don't equal points, and Benitez needs the January transfer window more than ever to add goals and steel to his squad.
He also needs certainty on the club's future ownership. The Spaniard, not to mention the Magpies' fans, will be praying Staveley's takeover is completed while they still have a chance to do something about their growing relegation fears.
Benitez says he still doesn't know his budget for next month. He needs clarity fast.
Everton's first win on the road in 17 attempts - stats
◾Newcastle have picked up just one point in their last eight Premier League games (W0 D1 L7).
◾Everton have collected 10 points in their last four Premier League games - one more than they managed in their previous 12 (9).
◾Everton ended a run of 16 Premier League away games without a win (D8 L8), claiming their first victory since winning 1-0 at Sam Allardyce's Crystal Palace in January.
◾Newcastle United have lost four consecutive home league games at St James' Park for the first time since April 2015 under John Carver.
◾Newcastle haven't won any of their last 44 home Premier League games in which they've gone in behind at half-time since winning 3-2 against Reading in December 2006.
◾Only one Newcastle player has received more red cards in a single Premier League season than Jonjo Shelvey this season (2) - David Batty in 1997/98 (3)