A hat-trick of first-half goals were key as Cork claimed their first league points at Pairc Ui Rinn tonight.
A brace from Paudie O'Sullivan and another three-pointer from Cathal Naughton had the Rebels 3-08 to 0-07 ahead at the break.
Waterford outscored their opponents by seven points to two in the third quarter, closing the gap to 3-10 to 0-14.
However, teenager Conor Lehane was a lighting light for Jimmy Barry-Murphy's men with seven points from play.
The visitors were hit hard by injuries and made four changes to the team listed in the programme.
Most of the absentees for Michael Ryan's Waterford side came in defence with Noel Connors, Aidan Kearney and Shane O'Sullivan ruled out.
Maurice Shanahan was unable to start in the Deise attack, with Philip Mahony, Stephen Daniels and two Prendergasts, Declan and Seamus, brought in.
Waterford began the game in impressive form and raced into a 0-03 to 0-00 lead inside six minutes with Paul O'Brien, Kevin Moran and Martin O'Neill on target.
But the Deise subsequently felt the brunt of the Cork attack as Ryan's charges struggled to cope with the forced changes to their rearguard, and in turn the quick thinking of the Rebels' forward lines.
Cork accumulated 1-06 without reply over the next 15 minutes. Patrick Horgan claimed the hosts' first score as he cut in from a tight angle, following good support play from Lehane.
UCC student Lehane then got on the scoresheet with a fine effort from 55 metres out and followed up on 11 minutes to tie the game at 0-03 apiece with another score from play.
The Midleton clubman again had a hand in Cork's next score, providing the scoring pass to Ben O'Connor after breaking free from the Deise cover.
Lehane was causing huge problems for Waterford and now at full-forward, he continued to fire scores from all angles.
His third point pushed Cork 0-05 to 0-03 ahead after 18 minutes, before Lehane passed the baton to Paudie O'Sullivan who suddenly became red hot for the Rebels.
O'Sullivan knocked over a 20th minute point before striking the first goal of the night from the resulting puck-out.
Ben O'Connor began the move after winning possession around the midfield sector. Pa Cronin was given plenty of space as he picked out O'Sullivan who blasted past Waterford goalkeeper Ian O'Regan.
Waterford ended a barren period for them with Pauric Mahony landing two quick points, but this came in the middle of a dominant Cork spell, with Barry-Murphy's side continuing to show no mercy.
Darren Sweetnam and Horgan added points to open up a 1-08 to 0-05 advantage, before it rained goals on a mild evening on Leeside.
Lehane and Naughton combined as the latter notched Cork's second goal in the 26th minute. Shane Casey hit a wide for Waterford, before O'Sullivan found the net to help Cork take a 3-08 to 0-05 lead.
Waterford bounced back before the break with Martin O'Neill and Mahony claiming points to reduce the arrears to 1- points at the turnaround.
The visitors picked off some nice scores from play and indeed just three of their 11 second half points came from frees.
Jamie Nagle, Ken Casey and O'Neill all registered points inside five minutes of the restart to ensure a 3-08 to 0-10 scoreline. Naughton hit back for Cork with his only point of the contest, but Waterford continued to press hard.
Shane Walsh struck a wide before O'Neill converted the first of his three second half frees. Cronin responded with his only score for Cork, but O'Neill and Mahony soon added to the Deise's tally.
Lehane kickstarted the final quarter in spectacular fashion with the score of the night, as he struck a fine ground shot over the crossbar from an acute angle. Horgan then extended Cork's lead to eight points with a 56th minute score.
Despite Waterford continuing to press with the likes of teenage substitute Gavin O'Brien taking two fine scores from play late on, an increasing wides tally certainly cost Waterford. They had 12 wides in all, with eight of those coming in the second half.
Lehane finished on a high by scoring three of Cork's final four points from play, capping off an encouraging first Division 1A win in Barry-Murphy's second stint as Cork manager.
Cork: C Lehane 0-07, P O'Sullivan 2-01, P Horgan 0-04, C Naughton 1-01, B O'Connor, D Sweetnam, P Cronin, S Og O hAilpin 0-01 each
Waterford: M O'Neill 0-05, P Mahony 0-04, G O'Brien 0-02, P O'Brien, K Moran, J Nagle, K Casey, S Prendergast, E McGrath, T Ryan 0-01 each
CORK: D Óg Cusack; S O’Neill, S McDonnell, B Murphy; J Gardiner, R Cashman, W Egan; S Óg Ó hAilpín, D Sweetnam; C Lehane, P Cronin, C Naughton; P Horgan, P O’Sullivan, B O’Connor.
Subs used: T Kenny for Sweetnam (49 mins), L McLoughlin for Gardiner (55), L O’Farrell for Naughton (64), B Corry for Lehane (68).
WATERFORD: I O'Regan; Philip Mahony, D Fives, S Daniels; J Nagle, K Moran, D Prendergast; S Molumphy, P O’Brien; S Prendergast, M Walsh, Pauric Mahony; M O’Neill, S Walsh, S Casey.
Subs used: E McGrath for S Walsh (half-time), P Prendergast for D Prendergast, G O’Brien for O’Neill (both 57 mins), T Ryan for Casey (63), D Twomey for S Prendergast (68).
Referee: Barry Kelly (Westmeath)