The Senegal international's drought finally ended 31 minutes into a pulsating encounter when he powered a header past goalkeeper Paddy Kenny to end a run stretching back to the 1-1 Europa League draw with Benfica on April 11.
However, the tie remained in the balance until deep into the second half when strike partner Yoan Gouffran blasted home to wrap up a 2-0 win over the Sky Bet Championship side.
Manchester United overcame rivals Liverpool 1-0 to reach the Capital One Cup last 16 on a night which saw holders Swansea bow out at Birmingham.
Javier Hernandez brought a sense of stability back to United after a turbulent week by netting the only goal of an absorbing tie at Old Trafford.
Following a heavy weekend derby defeat to Manchester City, Hernandez wriggled away from Jose Enrique to touch home Wayne Rooney's corner early in the second half of a game in which Luis Suarez impressed on his return from a 10-match suspension.
Arguably the biggest shock of this year's Capital One Cup came at St Andrew's, where Birmingham secured a shock 3-1 win against holders Swansea.
After a first half in which Wilfried Bony and Alejandro Pozuelo hit the post in quick succession, Blues appeared a different animal after the break.
Dan Burn headed home his first goal for the club in the 56th minute, before Matt Green added a second from close range soon after.
Inspired by winger Chris Burke, who played his part in all three goals, Tom Adeyemi also got in on the act with his maiden goal late on - with Bony netting a consolation with virtually the last touch.
Stephen Ireland marked his first Stoke start with a goal in the 2-0 victory at Tranmere.
One of seven changes made by manager Mark Hughes, the on-loan Aston Villa midfielder put them ahead in the 23rd minute at Prenton Park.
Peter Crouch, making his first start of the season, scored in stoppage time to seal a 2-0 victory which was somewhat harsh on the hosts.
Newcastle United Fixtures
September 30 20:00 Premier League Everton v Newcastle United
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
PREMIER LEAGUE
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
LEAGUE CUP
NEWCASTLE 2 LEEDS UTD 0
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