Hook sparked the Ospreys' second-half dominance
Ospreys (10) 34
Tries: Marshall, Hook, Bennett, Walker, Williams
Con: Hook (3)
Bristol (3) 3
The Ospreys charged into the EDF Energy Cup semi-finals after a superb second-half display against Bristol.
After both sides had exchanged early penalties, Justin Marshall scored the home side's first try to give them a slender 10-3 lead at the interval.
James Hook scored a superb solo try shortly after the break before Huw Bennett and Nikki Walker crossed in quick succession 10 minutes later.
Barry Williams then added a fifth try six minutes from time.
Marshall's opening try came on 13 minutes as the Ospreys pack gave an early indication of their superiority by driving the Bristol pack over their own try-line.
Former All Blacks scrum-half Marshall then had the simple task of diving on the ball to score.
Hook converted but then missed two penalties attempts, the second of which brought an uninspiring first half to a close.
But the rising star, who lined-up at inside centre, illuminated the evening with a dazzling try two minutes after the break.
The 21-year-old raced onto the ball just inside Bristol's half, and a couple of dummy-passes and side-steps took him clean through the visiting defence.
The resulting conversion in front of the posts was a formality and the Ospreys were clear at 17-3.
The result was put firmly beyond doubt 10 minutes later when the Welsh region added two further tries.
Hooker Bennett scored first when he emerged from the bottom of forceful driving maul and then winger Walker showed great strength and speed to round off a superb flowing move in the right corner.
Hook missed the first conversion, and Shaun Connor fared no better when he was then handed the kicking duties.
The Ospreys rounded off a thoroughly dominant second-half performance when replacement hooker Williams dived over under the posts after another superb handling move for a fifth try.
Ospreys coach Lyn Jones:
"There is a lot more to come from us, we can all see that.
"Bristol were organised and they are well coached, and I thought they would be good enough to score 20 points against us.
"I would like to play Leicester [in the semi-finals] with what happened in the Heineken Cup last season."
Bristol head coach Richard Hill:
"Overall, I was pretty pleased with the performance.
"They had their scoring patch for 10 minutes at the start of the second half, and the game settled down again.
"I thought there were some brave performances from the players, and it is all about coming down to places like this and learning from the experience."
Ospreys: Byrne; Vaughton, Selley, Hook, Walker; Connor, Spice; D Jones (capt), Bennett, C Griffiths, AW Jones, Bateman, Tiatia, Tandy, R Jones.
Replacements: B Williams, Millward, Cockbain, Lloyd, Roberts, Henson, Bishop.
Bristol: Arscott; Stanojevic, Cox, Taumalolo, Pozzebon; Strange, O'Riordan; Clarke, Blaney, Thompson, Sambucetti, Hohneck, Lewis, Short (capt), To'oala.
Replacements: Nelson, Irish, Attwood, Martin-Redman, Nicholls, Griffiths, Reay.
Referee: Tim Hayes (WRU)