Teenager Adam Armstrong and midfielder Gael Bigirimana were also on target in the Under-21 Premier League fixture at The Hawthorns.
Director of football Kinnear watched from the stands as Willie Donachie’s side came from behind to win.
Bigirimana gave United an early lead with a 35-yard effort, but West Brom struck twice inside a minute and took the lead, only for Vuckic to level in the 25th minute.
Morgan Ferrier gave the home side a 3-2 half-time advantage, but Vuckic netted a second equaliser in the 75th minute, and highly-rated teenager Armstrong, 16, scored a dramatic winner late in the game.
Defender Remie Streete, from South Shields, was also in Donachie’s team along with James Tavernier and Curtis Good.
NEWCASTLE UNITED: Alnwick, Tavernier, Streete, Good, Gillesphey, Bigirimana, Vuckic, Aarons (Roberts, 55), Armstrong, Quinn, Campbell.
Newcastle United Fixtures
October 5 15:00 Premier League Cardiff City v Newcastle United
October 19 12:45 Premier League Newcastle United v Liverpool
October 27 13:30 Premier League Sunderland v Newcastle United
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NEWCASTLE UNITED 2013/14
EVERTON 3 NEWCASTLE 2 (Cabaye, Remy)
Krul, Debuchy, Yanga-Mbiwa (46' Williamson), Coloccini, Santon, Tiote, Anita (69' Cisse), Ben Arfa (46' Cabaye), Sissoko, Gouffran, Remy
Subs: Elliot, Obertan, Sammy Ameobi, Dummett
NEWCASTLE 2 HULL CITY 3 (Remy 2)
Krul, Debuchy (86' Tiote), Yanga-Mbiwa, Coloccini, Santon, Cabaye (62' Gouffran), Anita, Sissoko, Ben Arfa, Cisse (73' Marveaux), Remy
Subs: Williamson, Elliot, Sammy Ameobi, Dummett
ASTON VILLA 1 NEWCASTLE 2 (Ben Arfra, Gouffran)
Krul, Debuchy, Coloccini, Yanga-Mbiwa, Santon, Anita (74' Tiote), Cabaye (88' Sammy Ameobi), Ben Arfa, Sissoko, Remy (63' Gouffran), Cisse
Subs: Elliot, Marveaux, S Taylor, Dummett
NEWCASTLE 1 FULHAM 0 (Ben Arfa)
Krul, Debuchy, Yanga-Mbiwa, Coloccini, Santon, Ben Arfa, Sissoko, Anita 65' (Cabaye), Marveaux 74' (Remy), Shola Ameobi 65' (Gouffran), Cisse
Subs: Gosling, Elliot, Sammy Ameobi, Dummett
NEWCASTLE 0 WEST HAM 0
Krul, Debuchy, Yanga-Mbiwa, Coloccini, Santon, Ben Arfa, Sissoko, Anita, Marveaux 66' (Sammy Ameobi), Shola Ameobi, Cisse 72'
Subs: Gosling, Bigirimana, Elliot, Vuckic, Dummett
MAN CITY 4 NEWCASTLE 0
Krul, Debuchy, Coloccini, S Taylor, Yanga-Mbiwa, Sissoko, Tiote, Gouffran 45+4' (Dummett), Ben Arfa 65' (Sammy Ameobi), Gutierrez 44' (Anita), Cisse
Subs: Elliot, Marveaux, Shola Ameobi, Obertan
NEWCASTLE 2 LEEDS UTD 0 (Cisse, Gouffran)
Krul, Debuchy, Williamson, Coloccini, Dummett, Gouffran (90' Vuckic), Anita (80' Gosling), Tiote, Marveaux, Sammy Ameobi, Cisse (71' Obertan).
Subs: Ben Arfa, Yanga-Mbiwa, Bigirimana, Alnwick
MORECAMBE 0 NEWCASTLE 2 (Shola Ameobi, Sammy Ameobi)
Elliot, Debuchy, Yanga-Mbiwa, Good, Dummett, Bigirimana, Gosling, Marveaux 88' (Sissoko), Vuckic 46' (Shola Ameobi), Sammy Ameobi, Gouffran 71' (Ben Arfa)
Subs: Santon, Anita, Alnwick, Streete