Davies, making his return to action after a 16 month battle to overcome a knee injury, raced on to a flick from Sylvan Ebanks-Blake to score with a low 106th minute drive.
It broke the hearts of Accrington who had been kept in the tie by a superb display from goalkeeper Kenny Arthur.
Accrington stalwart Paul Mullin had given League Two Stanley a shock 40th minute lead and it took Wolves until the 73rd minute to draw level through Chris Iwelumo.
When Iwelumo struck again 12 minutes into extra time, Wolves looked set to cruise to victory.
But Accrington refused to buckle and stunned Wolves again through an Ian Craney strike before Davies finally ended their challenge.
Arthur initially kept Wolves at bay with two stunning early saves which laid the foundations for Mullins' shock opener.
He tipped away a close range header from Neill Collins and pushed a 30 yard drive from David Edwards over the bar 15 minutes later.
Accrington were able to cash in on Arthur's heroics in stunning fashion five minutes before half-time when Jamie Clarke beat goalkeeper Wayne Hennessey from 20 yards only to see his drive crash off the post.
But the rebound flew straight to the unmarked Mullin who dived low to steer his header into an empty net.
Predictably, Wolves laid siege to the Accrington goal in the second-half but Arthur proved to be in inspired form.
In the space of 60 seconds he beat out a shot from Iwelumo, a header from George Elokobi and a fierce drive from Edwards.
But there was nothing he could do when Keogh surged down the left wing and delivered a pin-point centre that Iwelumo headed home from six yards to take the game into extra time.
Iwelumo showed his power in the air again when he converted a Davies corner but that was still not enough to finish off Accrington.
Craney raced on to a long through ball from Leam Richardson and drilled a low drive beyond Hennessey only for Davies to
then finally end their resistance.