Roscommon looked to have weathered the early Clare storm when leading by five points with injury-time approaching, but man-of-the-match Keelan Sexton slotted home a penalty before Jamie Malone fired the winner soon after.
It was heartbreak for Roscommon, but ecstasy for Clare as Collins leads them into the last eight for a second time after also making the quarter-finals in 2016, and they now have two weeks to prepare for a date with a big hitter at HQ.
Cathal O'Connor surged forward to kick the opening point of the game and that was a sign of things to come in a free-flowing contest that went from one end to the other in rapid-fire fashion.
Roscommon had the ball in the net in the sixth minute when Diarmuid Murtagh, a late replacement for Cathal Heneghan, reacted best to a shot from Conor Cox that dropped short, as he fisted to the net.
Clare fired the next two points through Sexton (free) and corner-back Cillian Rouine to quickly draw level, though, and they had the better of the first-half exchanges.
Sexton put them two points to the good midway through the half when a beautiful pass from Ciarán Russell played him through on goal and while his effort was scrambled, it found its way over the line as they led 1-4 to 1-2.
Their lead got as big as four on two occasions in the opening half with O'Connor pulling strings in midfield and Pearse Lillis doing an effective man-marking job on Roscommon danger man Enda Smith, but the Murtagh brothers kept the Connacht side in it.
Ciaráin Murtagh fired over three lovely points form play while Diarmuid was on target from placed balls as they trailed by two points at the break, 1-10 to 1-8, despite playing second fiddle to the Banner men.
The gap was quickly out to three upon the resumption when Sexton stroked over a lovely free from distance, but Collins' side would go the next 24 minutes without a score as the Rossies took complete control.
Cunningham's side fired over the next six points without reply, with Ronan Daly surging forward to fire over two beauties as they made their game-winning move and Clare had to wait until the hour mark to finally stem the bleeding.
That was another Sexton free but the Banner looked dead and buried when Ciaráin Murtagh put five between the sides in the 67th minute, 1-17 to 1-12.
Clare hadn't read the script, though, as Cleary cur the gap to four from a free before substitute Gavin Cooney was pulled down a minute later, with Sexton rifling the resultant penalty to the net to leave just one in it.
Sexton sent over a huge free to level it two minutes later before Malone ventured forward from defence to fire over a dramatic winner in the final minute of injury time for a famous victory.
SCORERS - Clare: K Sexton 2-6 (5f, 1-0 pen), C O'Connor 0-2, E McMahon 0-2, P Collins 0-1, C Rouine 0-1, E Cleary 0-2f, J Malone 0-1
Roscommon: D Murtagh 1-2 (2f), C Murtagh 0-5 (1f), R Daly 0-2, C Cox 0-1f, N Kilroy 0-1, C McKeon 0-1, C Daly 0-1, D Smith 0-2 (1f), R Hughes 0-1, K Doyle 0-1.
CLARE - T O'Callaghan; C O'Dea, M Doherty, C Rouine; A Sweeney, C Russell, J Malone; D O'Neill, C O'Connor; P Collins, E Cleary, E McMahon; P Lillis, A Griffin, K Sexton.
Subs: B Rouine for Sweeney (53), D Tubridy for Griffin (54), G Cooney for Collins (61), C Jordan for McMahon (66)
ROSCOMMON - C Lavin; D Murray, B Stack, C Daly; C Hussey, R Daly, N Daly; U Harney, E Dolan; N Kilroy, C Murtagh, E Smith; D Murtagh, C Cox, C McKeon.
Subs: R Hughes for Hussey inj (42), D Smith for Cox (47), K Doyle for Kilroy (58), A Glennon for D Murtagh (64), E McCormack for McKeon (68)
REF - N Cullen (Fermanagh)