Dragons dreams of European glory ended at the quarter-final stage as a ruthless Bristol claimed a 56-17 victory at Ashton Gate.
Dean Ryan’s men made a stunning start to the last eight showdown with wing Ashton Hewitt scoring early on after sensational vision from Sam Davies.
But a devastating hat-trick of tries in six shuddering first half minutes – as the stars of Bristol lit up in stunning fashion – saw the home side wrestle back control by the break.
Captain Rhodri Williams scored a fine solo effort for Dragons in the second half, as he sniped over under the posts as the visitors continued to battle away bravely.
However, it was the Bears who booked a semi-final berth against either Bordeaux-Begles or Edinburgh as the pulled away in the closing stages with another late burst of scores.
The final scoreline was harsh on Ryan’s men who posed plenty of problems and the region will still look back on the whole European season as a success after emerging from a difficult pool to secure knockout rugby.
Dragons were huge underdogs, but they began on the front foot and took the lead after a superb clearing kick from Williams forced Charles Piutau into an error and Sam Davies slotted a penalty.
The fly half then turned provider with a sublime cross field kick that found Hewitt in space and he brushed off Piuau to race over.
Bristol hit back in stunning style as Piutau made a break away in midfield and the Bears eventually made numbers count wide right as Nathan Hughes scored and Sheedy converted.
The home side had suddenly clicked and another sweeping move ended with on-loan back row Ben Earl touching down.
Moments later Earl was the beneficiary of another stunning Semi Radradra offload, after Harry Thacker had burst clear down the left, to stretch the lead to 21-10 after a painful five minutes.
Sheedy nudged the Bears further ahead with three points, after Dragons strayed offside, as Dragons looked for a foothold back into the game.
Big carries from Jamie Roberts and Aaron Wainwright rocked Bristol back, but the home defence held firm in the dying moments of the first half.
Bristol started the second half at real pace, offloading at every opportunity and scored a brilliant fourth as Radradra timed a run to perfection and then raced away from tacklers to score.
A classy response from Rhodri Williams, against his former club, saw him snipe around a ruck to dart past Chris Vui and under the posts.
Roberts was hauled up agonisingly short, after Nick Tompkins did well to roll out of a tackle, as Dragons threatened a third.
But it was Bristol who would finish in style with late scores from Vui, Max Malins and Dan Thomas taking them past the half century.
11m Davies p 0-3
13m Hewitt t Davies c 0-10
20m Hughes t Sheedy c 7-10
24m Earl t Sheedy c 14-10
26m Earl t Sheedy c 21-10
30m Sheedy p 24-10
42m Radradra t Sheedy c 31-10
51m Williams t Davies c 31-17
55m Sheedy p 34-17
70m Sheedy p 37-17
74m Vui t Sheedy c 44-17
75m Malins t Sheedy c 51-17
77m Thomas c 56-17
Bristol: Charles Piutau (Malins 50), Luke Morahan, Semi Radradra (Leiua 72), Piers O’Conor, Henry Purdy, Callum Sheedy, Andy Uren (Randall 53); Jake Woolmore (Thomas 49), Harry Thacker (Capon 66), Kyle Sinckler (Afoa 49), Dave Attwood (Joyce 63), Chris Vui, Steve Luatua, Ben Earl, Nathan Hughes (Thomas 49)
Replacements: Will Capon, Yann Thomas, John Afoa, Joe Joyce, Dan Thomas, Harry Randall, Max Malins, Alapati Leiua
Dragons: Jordan Williams (Lewis 62); Jonah Holmes, Nick Tompkins (Warren 78), Jamie Roberts, Ashton Hewitt, Sam Davies, Rhodri Williams (Baldwin 72); Brok Harris (Reynolds 61), Elliot Dee (Hibbard 61), Leon Brown (Fairbrother 61), Joe Davies (Maksymiw 70), Matthew Screech, Aaron Wainwright, Harri Keddie (Basham 56), Ross Moriarty.
Replacements: Richard Hibbard, Josh Reynolds, Lloyd Fairbrother, Joe Maksymiw, Taine Basham, Luke Baldwin, Josh Lewis, Adam Warren
Referee: Mathieu Raynal (France)