In the most wretched of conditions, they survived a tremendous second-half fight-back by the Leesiders, who paid the penalty for some dreadful finishing.
Offaly, who qualified for this semi-final by virtue of winning the B grade, produced a gutsy performance. Playing no-nonsense hurling in the difficult conditions, they knocked a highly-rated Cork team out of their stride with the ferocity of their challenge.
Cork's decision to play against the elements looked the correct choice after Kevin Canty rifled home a goal to give his side a 1-1 to 0-1 lead after 10 minutes.
However, Cork's persistence in trying to play fancy hurling in the appalling conditions was totally the wrong option and Offaly's more direct play soon began to pay. They pinned Cork in their own half for long periods and with Shane Dooley, son of former Offaly star Joe, sparkling in attack, the Leinster champions were level at the end of the opening quarter.
Cork struggled in most sectors, particularly in attack, where the Offaly defenders, notably Thomas Coughlan and Ciarán Flannery, were completely on top.
The near galeforce wind was clearly a huge advantage and Ciarán Slevin's goal in the 17th minute reflected Offaly's out-field superiority.
Cork were under enormous pressure for the remaining minutes of the half, and Offaly were denied a second goal by alert Cork 'keeper Richard Cunningham, who denied Ger Treacy.
It mattered little, however, as Offaly continued to press home their advantage, and five points without reply - two from the impressive Dooley left them 1-9 to 1-2 in front at half-time.
The second-half developed into a titanic struggle as Cork set about whittling down the deficit. However, while they kept Offaly in their own half for most of the second period, the scores did not come as often as they would have liked, principally due to heroic defending by Coughlan, Flannery and Kevin Grogan.
In a breakaway attack, Ciarán Slevin pointed for Offaly, their only score of the half, and what an invaluable one it turned out to be. However, Cork continued to press and at the end of the third quarter, there were just three points between them, 1-10 to 1-7.
As the tension mounted, the Offaly defence was under enormous pressure and two Cork points reduced the deficit to the minimum as time ticked away.
In a welter of excitement, the magnificent Offaly defence held firm for a famous victory and a place in the final against Tipperary.
: Offaly - C. Slevin 1-3 (0-1 free), S. Dooley 0-3, D. Molloy, S. Clancy, G. Kelly, K. Grogan 0-1 each. Cork - B. Canty 0-5 (frees), K. Canty 1-1, C. Keane 0-2, D. O'Callaghan 0-1.
: S. Martin; J. Cashin, T. Coughlan, C. Flannery; C. Hernon, K. Grogan, J. Corrigan; S. Dunne, J. Ryan; S. Dooley, D. Molloy, G. Kelly; C. Slevin, S. Clancy, G. Treacy. Subs: J. Maher for Cashin, D. Heagney for Kelly.
: R. Cunningham; G. O'Driscoll, J. Seward, B. Coleman; R. O'Flynn, B. Sheehan, R. Cashman; D. Kelleher, E. Manning; B. Canty, C. Keane, C. O'Leary; D. O'Callaghan, K. Canty, F. Corcoran. Sub: C. Daly for Kelleher.
: W. Barrett (Tipperary).