They scored five first-half tries to claim third place in the tournament after losing 21-18 to Castres on Friday night.
Jon Goodridge, James Forrester (2), Mark Foster and summer signing Rob Thirlby scored the tries with Ludovic Mercier converting four of them - his other attempt hitting the post.
In a fiesty encounter, Rob Elloway, Adam Eustace and Patrice Collazo were all yellow-carded at various points of the four-quarter game.
It is doubtful that Hazell will face any suspension after his dismissal, which happened after a 22-man brawl broke out right at the start of the game.
Hazell and Leeds' Richard Parks were picked out, and dismissed.
Both sides were allowed to return to 15 men at the end of the first quarter, with Gloucester 14-5 up, but Hazell and Parkes were not allowed to take any further part in the game.
Gloucester scored their first try after six minutes, and it was created by one of the youngest players on show.
Former St Peter's School pupil Jack Adams, 18, on his first XV debut, made a superb jinking run from his own half.
He side-stepped three Leeds tacklers and darted 20 metres into space and after bumping off the final tackler he offloaded to Goodridge, who scored between the posts to hand Mercier an easy conversion.
After 12 minutes Gloucester were 14-0 up after a flowing back-line move orchestrated by Henry Paul, back after his knee injury, and Mercier.
They took Gloucester into Leeds territory and earned a line-out, which was won by Gloucester and they rolled over, with Forrester coming up with the ball.
A superb touchline conversion from Mercier gave Gloucester a good cushion.
Gloucester went down to 13 men when Eustace was yellow-carded for a professional foul on the floor in a ruck, and Leeds hit back when Tom Biggs scored a try.
After the end of the first quarter, the two sides were allowed back to full strength, Jake Boer coming into Gloucester's back row.
But there was no let-up in Gloucester's threat, and they moved 19-5 ahead after 28 minutes with another try.
Foster and Paul combined well in the Leeds half and moved the ball forward.
Paul's vision found Forrester on the wing with a looping 30-metre pass and the number eight scampered in for his second try, Mercier hitting the post with his conversion attempt from the touchline.
Gloucester really had their tails up now and won turnover ball in their own 22, and Goodridge got the ball on his own try-line and cleared upfield with his right boot.
Foster went after it, and took the ball first bounce to wrongfoot the Leeds back three and score, Mercier adding the extras for a 26-5 advantage.
There was still time for another Gloucester try before half-time.
It came after 34 minutes when summer signing Rob Thirlby cut inside the Leeds half-backs on halfway and the outpaced the winger and full-back to score, Mercier converting to hand Gloucester a 33-5 half-time advantage.
Andre Snyman scored a 67th-minute try for Leeds, converted by Roland de Marigny, while Gloucester were again down to 14 men, Collazo spending 10 minutes in the bin after an altercation at a scrum.
Both sides ended the match as they started, with 14 men, as Elloway was the last Gloucester man to see yellow, sitting out the last four minutes along with his Leeds opposite number after another disagreement at a scrum.
David Rees had the last word with a last-minute try, converted again by de Marigny.
Coach Dean Ryan did not comment on Hazells dismissal, but of the game he said: "It was a rejuvenated back-line with Ludovic Mercier and Henry Paul returning, coupled with a great scrum presence with Patrice Collazo.
"That laid the foundations.
"I was pleased with Haydn Thomas and Jack Adams on their debuts, while Rob Thirlby and Mark Foster have played two full games in two days."
Gloucester: J. Goodridge, M. Foster, J. Adams (A. Allen 20), H. Paul, R. Thirlby, L. Mercier (R. Lamb 60), H. Thomas (P. Richards 60), P. Collazo, M. Davies (R. Elloway 60), T. Sigley (G. Powell 60), A. Eustace, M. Cornwell (A. Brown 40), P. Buxton, A. Hazell (sent off 1, J. Boer 20, O. Azam 76), J. Forrester (T. Sigley 69-74).