The Newport-Gwent Dragons did Welsh city rivals Cardiff Blues a huge favour by holding off Connacht on Saturday.
Dragons: (12) 24:
Tries: Morgan (2), Forster, Breeze.
Cons: Sweeney 2.
Connacht: (7) 19:
Tries: O'Sullivan, Jackman, O'Connor.
Cons: Warwick 2.
The Irish side's loss at Rodney Parade means that the Blues and not Conancht will go into a play-off against an Italian side for a Heineken Cup place.
The Dragons' own reward is a home tie in the Celtic Cup quarter-finals.
Kevin Morgan (2), Jason Forster and Ben Breeze all crossed, while Connacht had scores from John O'Sullivan, Bernard Jackman and Brendan O'Connor.
Connacht's bid to find a bonus-point win and finish above the Blues in the Celtic League got off to the worst of starts as they conceded a try in the first minute.
Mark McHugh dropped the ball in midfield, allowing Dragons scrum-half Gareth Baber to grab the loose ball and send skipper Forster over for an unconverted try.
A marginal forward pass decision from referee David Changleng prevented Ceri Sweeney from adding a swift second try for the home side.
The fly-half then missed a simple penalty as the half-hour mark approached.
Sweeney's wonky radar looked like it might cost the Dragons, as Connacht took the lead when Chris Keane jinked through to send O'Sullivan over the whitewash.
Paul Warwick's conversion put Connacht into a 7-5 lead, but deep in first-half injury time Breeze dived over in the left corner for a try that Sweeney converted.
Two quick-fire tries after the break from Morgan, one converted, looked to have put the tie beyond Connacht.
But the Galway side staged a superb rally in the dying moments of the match that had nerves jangling in two Welsh cities.
First replacement Jackman enjoyed a fortunate bounce from a kick ahead to plunge over with two minutes of regulation time remaining.
Then O'Connor picked a super angle in midfield to lance through the Dragons defence for a seven-pointer.
That put Connacht just 24-19 behind, but despite seven minutes of injury time they were unable to find one more converted try to snatch a dramatic victory.
Dragons: K Morgan; G Wyatt, P Montgomery, J Bryant, B Breeze; C Sweeney, G Baber; R Snow, S Jones, C Anthony, I Gough, L Charteris, J Ringer, J Forster (capt), M Owen.
Replacements: J Richards, A Black, R Thomas, P Sidoli, R Oakley, S Tuipulotu, C Warlow.
Connacht: M Mostyn, C McPhillips, M McHugh, J Downey, D Yapp; P Warwick, C Keane; R Hogan, J Fogerty, P Bracken, C Short, A Farley (capt), B O'Connor, M Lacey, J O'Sullivan.
Replacements: B Jackman, S Knoop, M Carroll, M Swift, M Walls, E Elwood, D Slemen.
Referee: David Changleng (SRFU).