These teams were well aware of each other’s strengths and weaknesses after meeting in the Carabao Cup four days earlier, with Everton winning 3-1, and the visitors started brightest as they hunted another victory.
However, they failed to test Lukas Hornicek, and Newcastle almost took advantage in the 17th minute when Dan Burn - who scored the Magpies’ consolation goal in the previous clash - headed wide at the far post from a corner.
Everton remained on top, and Merlin Rohl blazed over before Barry spurned a golden opportunity when he miskicked from close range with only Hornicek to beat.
The home fans became restless as their side struggled to find their rhythm, but they almost had something to cheer as Joelinton thumped a swerving shot just wide five minutes before half-time.
Harrison Armstrong sliced wide from 12 yards deep in stoppage time to sum up a drab opening 45 minutes, although that was perhaps unsurprising, with Everton’s league matches this season producing just four first-half goals.
Neither team registered a shot on target in the first half, but the Toffees finally made their dominance pay four minutes after the restart when they opened the scoring.
Tyrique George’s shot squirmed through Hornicek’s grasp, allowing Barry to tap home his eighth goal of the season across all competitions, as he scored against Newcastle for the third successive game.
Everton did not let up, and Jarrad Branthwaite saw a header saved by Hornicek, who then tipped Kiernan Dewsbury-Hall’s curling effort over the bar, moments before denying Jake O’Brien from the resulting corner.
The Magpies rallied and came agonisingly close to an equaliser when Anthony Elanga slid in at the far post, only to see the ball bounce along the goal line before it was hacked away.
Jacob Ramsey then flashed a volley wide from 20 yards, with Jordan Pickford saving Yoane Wissa’s shot with his legs late on, but a deeply disappointing night for Matthias Jaissle’s side was capped by a red card for Ramsey deep in stoppage time after a pair of quickfire bookings.
The defeat is Newcastle’s fourth in five games (W1), increasing the heat on Jaissle, and their 22nd in their last 33 Monday-held Premier League matches (W7, D4).
They fall one place to 13th, while Everton climb seven places to seventh after winning on three successive league visits to Newcastle for the first time - with this their first on the road in the Premier League since triumphing here in February.
Flashscore Man of the Match: Kiernan Dewsbury-Hall (Everton)
