Victor Anichebe scored a fine winner moments after coming off the bench as Everton came from behind to beat Newcastle 2-1 in a breathless contest at St James' Park.
Papiss Cisse headed Newcastle ahead inside two minutes and the Magpies could have doubled their lead when James Perch's header struck the post.
Everton levelled soon before the break when Leighton Baines beat Tim Krul with a magnificent free-kick from 30 yards.
The visitors struck a winner on the hour with another silky finish, with Anichebe tucking in after Baines and Nikola Jelavic combined superbly.
The imminent departure of Demba Ba to Chelsea is yet another headache for Newcastle manager Alan Pardew. Since the manager signed an eight-year deal to stay at the club until 2020, the Magpies have been in freefall, now winning just three of their last 17 Premier League games.
While Ba’s impending move is a blow, it could prove a blessing for his compatriot Cisse, who has often been in Ba’s shadow since moving from Freiburg for £8 million in 2011.
And Cisse proved there could be life after Ba when he headed Newcastle in front inside two minutes. Latching onto Krul’s hopeful punt forward, Cisse exploited Everton’s static defending to send a looping header over Tim Howard and into the net.
Cisse could have doubled his tally moments later when Shola Ameobi tore down the left and flashed a low ball across goal that the Senegalese striker was inches away from poking in.
The match ebbed and flowed after Newcastle’s blistering start, with Everton settling and creating chances, with Baines drawing a first class save out of Krul with a free-kick from 25 yards.
Baines’s moment was to come, but chances fell to Steven Pienaar, whose shot was smothered by Krul, and Marouane Fellaini, who was played in by Pienaar, but saw his shot courageously blocked by Davide Santon.
Newcastle came agonisingly close to moving ahead when Perch’s header from Vernon Anita’s pinpoint free-kick crashed back off the inside of the post, with Howard beaten.
With a relentless first half drawing to a close, Everton levelled in emphatic style. Baines stepped up to thrash a fierce, swerving effort over the wall and into the far corner. It was a goal of the highest quality that stunned St James’ Park.
The second half was less frantic but no less entertaining as both teams threw everything at the other in search of a winner. The game hinged on Ameobi’s miss just before the hour. Collecting Sylvain Marveaux’s beautiful lofted through ball with a superb first touch, Ameobi could only prod his shot wide from eight yards.
Everton punished Newcastle in ruthless fashion, hitting them with a sucker punch a couple of minutes later. Baines and Jelavic combined superbly down the left to create the chance and Anichebe, who was sent on just two minutes earlier by manager David Moyes, calmly stroked in from Jelavic’s cross.
Chances came and went for Gabriel Obertan and Cisse, but Newcastle lacked the cutting edge in front of goal that Ba has provided in the last two years, as Everton hung on for an impressive win, their first back-to-back away victories since 2011, to move above Arsenal and to within two points of a Champions League place. Newcastle are just two points clear of the relegation zone.
MAN OF THE MATCH
Leighton Baines (Everton) - Stunning free-kick capped a master class in attacking full-back play.
Newcastle: Krul 7; Perch 7, Williamson 6, Coloccini 6, Santon 7; Obertan 6, Anita 6, Tiote 6, Marveaux 7; S Ameobi 7, Cisse 7. Subs: Bigirimana 6, S Ameobi 6, Ranger N/A
Everton: Howard 8; Heitinga 7, Jagielka 7, Distin 8, Baines 9; Naismith 6, Neville 7, Osman 6, Pienaar 7; Fellaini 8; Jelavic 7. Subs: Anichebe 8, Oviedo N/A