Kilkenny qualified for the Division 1A Hurling semi-final thanks largely to four second-half points from Richie Hogan in a rip-roaring battle with Cork at Nowlan Park.
A late Conor Lehane goal pulled the Rebels within one point of the All-Ireland champions, but man of the match Michael Fennelly pointed late on to seal a third consecutive win for Brian Cody's side.
Luke O'Farrell's goal in the 46th minute had given Cork the upper hand as Kilkenny's poor finishing looked likely to cost them, but the Cats hit nine of the last ten points to accelerate to the win and the spot in the last four.
And in a repeat of last year's All-Ireland final, Kilkenny will meet Anthony Cunningham's Galway for a spot in the league final, while Cork must beat Clare in the relegation play-off to avoid the drop.
In the early stages it seemed as if Cork would run riot as the Rebels opened up a 0-4 to 0-1 lead by the 14th minute, with points from Lehane, Paudie O'Sullivan and Stephen Moylan.
Two dead-ball strikes from Eoin Larkin brought Kilkenny back into the tie, but another rapid-fire blitz from, Cork through Lehane, Moylan and Daniel Kearney, gave Jimmy Barry-Murphy's side a 0-7 to 0-3 lead by the 26th minute.
But the Cats went into half-time the stronger as two Larkin frees were added to by Lester Ryan and Colin Fennelly to leave it all square at 0-7 to 0-7 at the turnaround.
Immediately from the restart Richie Hogan, who also had a first-half penalty saved, got in on the act with a crisp point from play, but Cork hit back with their first point in 12 minutes when Pa Cronin found Paudie O'Sullivan in space.
In a game that, on occasion, touched on championship intensity, Luke O'Farrell looked to have edged the tie in Cork's favour 11 minutes into the second-half when he hit 1-1 in a minute.
Firstly, the nippy attacker struck a crisp shot past Eoin Murphy after some great work from Moylan and seconds later he showed JJ Delaney a clean pair of heels to score an equally fine point on the turn.
Those two scores gave Cork a three-point lead, but from then on Cody's men reacted to the prospect of defeat to put in their best spell of the game.
Five points in a row – including one from a penalty from Richie Power - saw Cody's side hold a two-point lead and, after Horgan halted their change with a free, they hit another three unanswered points to take total control.
Lehane, who tormented Kilkenny throughout, goaled in the 71st minute, but it was too late for the Rebels who miss out on a spot in the semi-finals and now must do battle with Clare to avoid the drop to Division 1B.
Kilkenny: E Murphy; C Fogarty, JJ Delaney, J Tyrrell; T Walsh (0-01), B Hogan, K Joyce; L Ryan (0-01), M Fennelly (0-01); W Walsh, E Larkin (0-06, 0-05f, 0-01'65), R Hogan (0-04); G Aylward, C Fennelly (0-04), A Fogarty.
Subs used: R Power (0-03, 0-01pen) for Aylward (27 mins).
Cork: A Nash; K Murphy, B Murphy, C O'Sullivan; L McLoughlin, C Joyce, S White; D Kearney (0-01), P Cronin; C Lehane (1-03), C McCarthy, P O'Sullivan (0-02); S Moylan (0-02), L O'Farrell (1-01), P Horgan (0-03, 0-03f).
Subs used: M Cussen for McCarthy (52 mins), C Spillane for B Murphy (57-60 mins blood), C Spillane for Kearney (65 mins).
Referee: Brian Gavin (Offaly).