The St Mary’s youngster finished a splendid move to the net after five minutes and then added two quick points, suggesting the Munster champions would win in a canter.
But Mayo, missing a number of regulars through illness or injury, hit back strongly, and inspired by the brilliance of wing-back Kevin Costello, quickly began to halt the Kerry charge.
Aidan Kilcoyne began the fight back with a point, and as Kerry began to waste possession, Mayo’s Mark Ronaldson ensured his side finished on level terms at half-time with a splendid goal just before the whistle.
On the restart, the Connacht men took the lead with excellent points by the impressive Kilcoyne, causing endless problems for the Kerry defence.
Kerry moved wing-back Joseph McGillacuddy in a bid to contain Kilcoyne, and he succeeded admirably. But the dominance of midfielder Sean O’Donnell kept the pressure on the Kerry defence, and only a superb fingertip-save by goalkeeper Brendan Kealy denied Mark Ronaldson his second goal in the 40th minute.
Surprisingly, for all their outfield dominance, Mayo weren’t to score again, as Kerry upped the tempo.
After Dan Doona tied the game for the fourth and final time with a point, Sheehan struck for the decisive score in the 55th minute.
A sweeping move from the Kerry half ended with Barry O’Grady racing through, but he was grounded by the Mayo keeper, and with team coach Pat O’Shea unable to watch, Sheehan made no mistake with the penalty.
Kerry added two further points, but there was still some defending to be done as Mayo made a late rally.
But McGillacuddy, Shane O’Sullivan and Padraig Reidy held firm, and Kerry will now meet Laois in the semi-final in a couple of weeks’ time.
Kerry coach O’Shea was extremely relieved to have survived the clash.
“They are a very good side and we knew that going into the game. When you reach this stage it’s all about getting a result and thankfully we did.”
“What I’m very happy with is that when the game was on the line with six or seven minutes to go, our lads showed great character in responding to the danger,” he said.
“Mayo put us under a lot of pressure in the second half and we responded very well.”
“They have a couple of outstanding players who posed a lot of problems for us, particularly in defence, but we put ourselves under enormous pressure by holding onto the ball too long, and that is something we’ll have to address for the semi-final.”
Scorers - Kerry: B. Sheehan 2-5 (1-5 frees); B. O’Grady, D. Doona 0-2 each; D. Breen 0-1.
Mayo: M. Ronaldson 1-2; A. Kilcoyne 0-5 (0-2 frees); J. Stenson 0-1.
KERRY: B. Kealy; M. Curran, L. Quinn, P. Reidy; C. Kelleher, S. O’Sullivan, J. McGillacuddy; D. Breen, S. O’Shea; M. Murphy, B. O’Grady, M. Bowler; D. Doona, B. Sheehan, D. Geaney.
Subs: B. Moran for O’Shea; J. Coffey for Curran; D. O’Sullivan for Bowler; J. Buckley for Geaney; S. Murphy for M. Murphy.
MAYO: R. Byrne; D. Padden, T. Howley, J. Conlon; K. Costello, D. Sloyne, S. Ryder; S. O’Donnell, H. McLoughlin; E. Tiernan, A. Kilcoyne, M. Conroy; S. Prendergast, J.G. Stenson, M. Ronaldson.
Subs: D. Coleman for Tiernan; C. Boyle for Prendergast; H. Gaughan for McLoughlin.
Referee: E. Murtagh (Longford).