The setback for Rafa Benitez's side, who scored a late goal through Daryl Murphy, means they stay top of the second-tier on 77 points on goal difference from Brighton & Hove Albion, who beat visiting Derby County 3-0 on Friday.
Huddersfield Town moved within six points of the leaders with a game in hand after a 1-0 win at Brentford thanks to Rajiv van La Parra's speculative 28th minute strike.
The Terriers moved five points clear of fourth-placed Leeds United, who were held 0-0 by Queens Park Rangers at Elland Road where the home side's ex-England keeper Rob Green, 37, made a fine first-half save on his 600th league appearance.
Leeds stay two points ahead of Reading, who lost 3-0 at fellow playoff-chasing team Preston North End after Tom Barkhuizen's brace for the home side.
Newcastle suffered a seriously lethargic off-day at St James' Park as Fulham, chasing a playoff spot after a recent run of good form, took the game to the leaders from the start.
Cairney put Fulham in front with a superb 20-metre strike into the top corner in the first half and after the teenager Sessegnon made his decisive contribution, a late goal from Murphy was just a consolation for the Magpies.
It could have been worse for Benitez's side as Tim Ream missed a penalty in added time for Fulham, who moved up to seventh only two points outside the playoff spots.
(Reporting by Ian Chadband; editing by Ken Ferris)
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