Two goals from Joshua Windass, who has scored 11 goals this season, earned the locals victory against a third-placed away side in the Premier League filled with substitutes in their starting eleven.
Windass scored his brace in the second half, in the 52nd and 65th minute, to give his side a definitive lead, although Bruno Guimaraes, in the 69th minute, put Newcastle closer to the scoreboard.
West Ham beat Brentford 1-0 thanks to a goal by Algerian Said Benhrama in the 79th minute.
West Ham and Sheffield Wednesday join Manchester United, Tottenham, Leicester, Southampton, Brighton, Fulham, Preston North End, Reading, Burnley, Fleetwood Town, among the teams already qualified for the next round Blackpool, Sheffield United, Sunderland, Ipswich Town , Wrexham and Grimsby.
Six Premier League teams were eliminated in the third stage, Crystal Palace, Everton, Bournemouth, Nottingham Forest, Newcastle and Brentford.
The match between Forest Green Rovers-Birmingham City has been postponed due to poor pitch conditions due to rain, while the duels Chesterfield-West Bromwich (3-3), Boreham Wood-Accrington Stanley (1-1), Luton Town – Wigan (1-1) and Liverpool-Wolwerhampton (2-2) ended in a draw and tiebreaks will have to be played.
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