Substitute Dan Shanahan flashed home the extra-time goal which drove Waterford to their ninth Munster SHC title in Thurles on Saturday.
In wet conditions, Shanahan blasted past Donal Og Cusack in the second period of extra-time to confirm the Deise’s first provincial success since 2007.
Eoin Kelly, who top-scored with 0-08, missed some late chances to win tonight's replay in normal time.
Ben O’Connor’s speculative goal from an angled free saw Cork fight back for a 1-11 to 0-14 stalemate, and one of their points came from a John Gardiner penalty which was deflected over.
But Waterford, helped by the introductions of Dan and Maurice Shanahan and Eoin McGrath, outlasted their great rivals in extra-time to earn the sweetest of victories in front of 22,763 spectators.
On the balance of play, Davy Fitzgerald's men deservedly pulled through to earn a place in the All-Ireland semi-finals and leave injury-hit Cork with just a week to regroup for an All-Ireland quarter-final clash.
As expected, Sean Og O hAilpin was unable to start due to a hamstring injury, so Shane Murphy was drafted into the defence and former footballer Michael Cussen replaced the injured Jerry O'Connor in the Rebels' attack.
Seamus Prendergast's inclusion in the forwards was Waterford's only change from the drawn game, Eoin McGrath being the player to make way.
The first half was similar to last week's opening period, in that Waterford's economical approach helped them hit the front and have the better of the half. Eoin Kelly was on the mark on three occasions as the Deise opened up a 0-03 to 0-01 lead, with Cathal Naughton registering Cork's first point.
Cussen was moved to centre-forward and Seamus Prendergast switched into the right corner on Brian Murphy, but Cork, although dominating around the half-back and midfield areas, struggled for scores. Indeed, by half-time, Naughton's opener was their only point from play.
Denis Walsh's side had the better of the exchanges in the half-backs and midfield, however they did not get the scores to show for it and three goal-scoring chances were also missed as Pat Horgan, Niall McCarthy and Aisake O hAilpin failed to find the net.
The best of them came in the 18th minute when Horgan flicked the ball around the advancing Clinton Hennessy, only for Noel Connors to retrieve the situation for Waterford with with a wonderful dive and clearance.
By that stage, John Mullane, who the Deise used as their furthest man forward, had landed his first point. It was a terrific length of the pitch score, with Michael 'Brick' Walsh and Declan Prendergast involved in the build-up. Cork responded with a free from Ben O'Connor who added a '65', and John Gardiner did likewise, to close the gap for Cork to 0-06 to 0-04.
Free-taker Kelly was Waterford's scorer-in-chief, taking his tally to five by the break, and Fitzgerald's charges went into the dressing room on a high, following a brilliant sideline cut from the right from midfielder Richie Foley. That gave them an 0-08 to 0-04 buffer, and Cork had further reshuffling to do at the rear, with Ray Ryan coming in for the injured Shane O'Neill.
The use of Stephen Molumphy as an extra midfielder had crowded the midfield for Cork and their telegraphed balls in towards O hAilpin gave the young target man little chance. But the Rebels bounced back strongly at the start of the second half, with the dark and damp conditions making it the first ever floodlit Munster SHC final.
After a Mullane shot had bounced back off a post, Cork raided forward for three successive points, two of them from lively substitute Paudie O'Sullivan. O hAilpin also increased his influence, laying off for Cussen to point and using his strength to create the second for O'Sullivan.
Kelly and O'Connor traded points before Foley struck Waterford's first wide in the 44th minute. That particular statistic showed the clinical nature of their play, but they could watch aghast when O'Connor picked off Cork's only goal.
Two minutes later, the Newtownshandrum clubman sent a flat, skimming shot a right wing free that caught goalkeeper Clinton Hennessy off guard and nestled in the top left corner of the net. On the greasy surface, O'Connor's strike looked like a mishit - he may suggest otherwise in the post-match interviews - but they all count, and it certainly was a rallying score for Cork.
It could have been a pivotal moment, but Waterford recovered quickly to lessen the blow. Substitute Brian O'Halloran, Kelly, Mullane and Shane Walsh scored four points in-a-row to have Fitzgerald's side back ahead at 0-13 to 1-08.
Mullane's 53rd-minute effort was just typical of the electric De La Salle forward. He showed great bravery to snaffle a catch and he then used his pace to race away from the cover and launch over a stunning point from close to the left sideline. Walsh also delighted the Waterford fans with a rousing catch and point.
O'Connor stopped the rot for Cork with a free and Naughton pointed from midfield to have the sides level for a second time at 1-10 to 0-13. Kelly pointed a free from a tight angle on the left to put Waterford in front again, only for Cork to win a 64th minute penalty as the advancing Cussen was clumsily brought down by Foley.
Up stepped Gardiner, his shot straight and true and a combination of Hennessy and Shane O'Sullivan diverted the ball over the crossbar for the concession of a point.
That made it 1-11 to 0-14 and that is how it remained until the final whistle, despite some last-ditch attempts at the posts from Kelly.
Cork lost their third first choice defender to injury when Ronan Curran was deemed unfit to take part in extra-time. Under-21 star William Egan took his place and pointed with his first touch, replying to the opener from Kevin Moran.
Waterford had started the first period of extra-time with a point from Moran after just 19 seconds, with Dan Shanahan, who was introduced for the injured Mullane, involved in the build-up.
As the rain got progressively heavier and handling conditions worsened, scores were really at a premium. Cussen sliced badly wide and on the cusp of half-time, defender Tony Browne, the goal-scoring hero from last Sunday, planted a long range free between the posts to give Waterford a 0-16 to 1-12 advantage.
The game slipped from Cork's grasp, three minutes into the second period, when Eoin McGrath helped break the ball through for fellow substitute Shanahan to drill a well-placed shot beyond the reach of Cork stopper Cusack. Waterford had one hand on the trophy.
Cork never let their effort slip though and following an O'Connor free which reduced the arrears to three points, Waterford had to defend a number of balls played in towards O hAilpin and company before referee Brian Gavin brought this battle of wills to a close.
Scorers: Cork: B O'Connor 1-05 (1-05f), C Naughton, J Gardiner (0-01 '65', 0-01 pen), P O'Sullivan 0-02 each, M Cussen, W Egan 0-01 each
Waterford: E Kelly 0-08 (0-06f), D Shanahan 1-00, J Mullane 0-03, R Foley (0-01 sl), B O'Halloran, S Walsh, K Moran, T Browne (0-01f) 0-01 each
CORK: D Óg Cusack; S Murphy, E Cadogan, B Murphy; J Gardiner, R Curran, S O’Neill; T Kenny, C Naughton; B O’Connor, M Cussen, N McCarthy; K Murphy, A Ó hAilpín, P Horgan.
Subs used: R Ryan for O’Neill (35+1 mins), P O'Sullivan for Horgan (half-time), L O'Farrell for K Murphy (66), W Egan for Curran (extra-time).
WATERFORD: C Hennessy; E Murphy, L Lawlor, N Connors; T Browne, M Walsh, D Prendergast; S O’Sullivan, R Foley; S Prendergast, K Moran, E Kelly; S Molumphy, J Mullane, S Walsh.
Subs used: B O'Halloran for S Prendergast (49 mins), M Shanahan for S Walsh (61), J Nagle for Lawlor (68), D Shanahan for Mullane (extra-time), E McGrath for O'Halloran (half-time, extra-time).
Referee: Brian Gavin (Offaly)
