The defending champions failed to score in the closing 20 minutes, but goals from Kieran McGrath and Tomás Costello in the first-half ensured their spot in the last four.
The city side looked to be well out of contention at half-time after they trailed 2-7 to 0-4 in shocking conditions./But a goal by substitute Eoin Teagle two minutes after the restart pulled them back to within six points of the champions.
Two quick scores from Corofin, including a fine point from Kieran Fitzgerald, gave them an eight point lead by the 36th minute, but amazingly the favourites only landed one score in the remaining action as St James set about cutting the deficit.
Conroy kicked his third point from a 45 and quickly landed a free to chop the Corofin cushion to six, and when Alan O’Donnell goaled for St James with ten minutes remaining the unlikely comeback looked on.
Conroy kicked two more frees in the closing five minutes, but Corofin’s experience saw them across the line 2-10 to 2-9 and into the semi-final of the championship, where they will meet Tuam Stars.
And the record winners of the Galway SFC, Tuam Stars, made easy work of beating Milltown, eventually running out 0-14 to 1-8 winners at Tuam Stadium.
For long stages it looked as if this tussle might be abandoned, such was the deluge of rain at the north Galway venue, but the sharpshooting of Shane Curtin (0-5) and Jamie Murphy (0-3) saw the 25-times winners into the last four.
An injury-time penalty was converted by Mark Hehir for Milltown, but Tuam Stars can now avenge their defeat in the final to Corofin last year after a wonderful team display.
Sean Armstrong proved the creative influence for Salthill-Knocknacarra who qualified for the semi-final after a 1-9 to 0-10 victory over An Cheathru Rua at Pearse Stadium.
After the sides went in level at half-time, Seamie Crowe struck the decisive goal immediately after the restart to give the 2004 champions a lead they would never relinquish.
Substitute Aonghus MacDonncha did his best to claw the Gaeltacht men back into the tie with two frees in the last ten minutes, but six points from Galway forward Armstrong and dual star Alan Kerins kicked Salthill-Knocknacarra’s final point, which eased them to the win.
And the seasiders will have to wait another week for the identity of their opponents in the next round after Killererin and Sean O Domhnaill’s Micheál Breathnach’s ended all square at Pearse Stadium.
Micheál Breathnach’s looked certain to have caused the upset of the weekend when Peadar Óg Ó Griofa goaled seven minutes into the second-half.
But three points in a row late on from Shane Hughes, Nicky Joyce – his sixth – and a Micheál Boyle free ensure the sides will have to meet again.