The £12m January signing’s first Magpies goal cemented a 3-1 win over the Toffees and ensured Frank Lampard’s first league game as manager ended in defeat.
Newcastle, backed by super rich new owners, spent £90m in January, while Leeds United only added an Under-23s striker.
And victory for Newcastle took them out of the bottom three onto 18 points, four adrift of 15th-placed Leeds United who are six points clear of the bottom three ahead of Wednesday night’s huge game at Aston Villa.
Unfortunate first-half own goals from Jamaal Lascelles and Mason Holgate had left Newcastle and Everton locked together at the break, but it was Newcastle, who handed a debut to £35m new boy Bruno Guimaraes as a late substitute, who eventually got themselves over the line courtesy of Ryan Fraser’s scruffy strike and Trippier’s effort in front of a passionate crowd of 52,186 at St James’ Park.
The win - just their third of the campaign, but second in succession - left them just a point behind Merseyside club, who succumbed despite the introduction of newcomers Dele Alli and Donny van de Beek from the bench.
Manchester United dropped out of the top four as Jay Rodriguez’s 100th career league goal - and first in 50 games - earned relegation-battling Burnley a well-deserved 1-1 draw at Turf Moor.
United dominated the first half as Paul Pogba, making his first Premier League start since his red card in the 5-0 capitulation to Liverpool in October, showed flashes of his brilliant best and fired the visitors in front with 18 minutes gone.
It was one of three times United had the ball in the Burnley net in the first half, with the other two ruled out, but momentum shifted radically in the second half after Rodriguez levelled in the 47th minute with the hosts then squandering chances to win it.
Sean Dyche will see it as a hugely encouraging point but will also know his side must soon find a way to accumulate them in threes if they are to survive - Newcastle’s win over Everton meant the gap to safety increased on the night to four points.
Watford, who are 19th, were beaten 1-0 by West Ham.