Newcastle's defeat means leaders Brighton & Hove Albion, who had beaten Queens Park Rangers 2-1 on Friday, remain two points clear at the top of England's second-tier league with five games remaining.
Both the top two, though, remain overwhelming favourites for automatic promotion to the Premier League.
Rafael Benitez's Newcastle almost opened the scoring in stunning fashion when Jonjo Shelvey hit the bar from the halfway line at the end of a breathless first half.
Against the run of play, Tom Lees then opened the scoring for Wednesday with a powerful header after the break before Steven Fletcher doubled the lead with an outstanding header.
Shelvey did pull a goal back in the 88th minute, taking advantage after Aleksandar Mitrovic's effort was spilled by Keiren Westwood but Wednesday held on.
Newcastle have 84 points, two fewer than Brighton, while Wednesday climb back into the play-off places in sixth place with 69 points.
Huddersfield Town, in third with 74 points, lost 2-0 to Nottingham Forest while fourth-placed Reading, a point behind, conceded six first-half goals in a crushing 7-1 defeat at Norwich City.
Leeds United, in fifth with 72 points, eased past Preston North End 3-0.
(Reporting by Tom Hayward; Editing by Ian Chadband)
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