Leighton Baines equalised with a stunning strike and substitute Victor Anichebe grabbed the winner to leave Newcastle deeper in trouble just outside the relegation zone.
With Demba Ba negotiating a move to Chelsea after an offer earlier in the day which triggered his release clause, Cisse took up the challenge of leading the Newcastle line and opened the scoring inside two minutes when he looped a header over Tim Howard after Everton had defended a long ball terribly.
Baines gave a glimpse of what was to come with a fabulous free-kick in the sixth minute which nearly drew Everton level, but on this occasion he was denied by an athletic one-handed save from Tim Krul.
Both sides carved out chances in an open first half, with Marouane Fellaini losing his balance when well placed to shoot inside the Magpies area and James Perch crashing a header against the post at the other end.
Newcastle had a confident penalty appeal turned down five minutes before the interval when Shola Ameobi thought he had been fouled by Phil Neville, but referee Martin Atkinson waved play on.
Everton equalised in sensational style in the 43rd minute as Baines stepped up to take a free-kick 30 yards from goal and beat Krul for power with a blistering piledriver that also swerved wickedly as it flew high into the net.
There continued to be nothing between the sides in the early stages of the second period, although Ameobi perhaps should have restored Newcastle's advantage when he poked wide after escaping from his defender.
The hosts were made to rue that miss on the hour mark as Anichebe made an instant impact barely a minute after coming on as a substitute, turning in Nikica Jelavic's cross from close range.
The onus was now on Newcastle to push forward and they did look vulnerable as they left spaces at the back, but Cisse almost made it 2-2 when his instinctive shot was well saved right on the goal-line by Howard after John Heitinga had blocked an initial header.
Krul had to back-pedal quickly to tip the ball over his crossbar after Mike Williamson had made a mess of trying to clear a Baines cross, while the Everton left-back curled another free-kick wide following a foul on Fellaini on the very edge of the box.
Newcastle piled on the pressure in the closing stages but Davide Santon's shot from a tight angle was kept out by Howard when he had the chance to square for an unmarked Cisse at the back post, and Everton held firm to seal victory and boost their European hopes.