The first half was a predictable affair given the conditions, steady rain and a greasy surface. The Tigers quickly adapted, pushing Bristol into conceding three penalties in the opening quarter, all punished by the accurate boot of John Liley.
The Tigers drove repeatedly into the Bristol ranks, usually in the guise of the centre Will Greenwood. There were also dangerous breaks from the scrum-half Austin Healey and the wing Steve Hackney.
Leicester's tighthead, Darren Garforth, burst like a raging rhinoceros out of a melee and charged at Paul Hull, showing no respect for the fact that Hull was appearing in his 100th League match, smashing into the full- back, but was hauled down by the fly-half Paul Burke.
Liley had landed a 49th minute penalty when, three minutes later, Healey broke from a ruck, slipped the ball to Greenwood who pounded through despairing Bristol cover before sending Hackney in at the corner for their first try. A second quickly followed when Stuart Potter went over under the posts.
Naturally Bristol did not give up and their persistence paid off when Richard Smith broke around a scrum and slid over for the touchdown. But then it was back to Leicester as Potter ran in his second try, Rob Liley was sent over and brother John did his stuff with the boot.
There was further Bristol defiance when David Tiueti scored a fine solo effort in the closing minutes, but it was too late as Leicester weathered a late storm for a deserved victory.
Bristol: Tries Smith, Tiueti; Conversion Burke. Leicester: Tries Hackney, Potter 2, R Liley; Conversions J Liley 3; Pens J Liley 4.
Bristol: P Hull (capt); D Tiueti, S Martin, M Denney, B Breeze; P Burke, R Smith; A Sharp, M Regan, D Hinkins, S Shaw, C Eagle, D Corkery, S Filali, C Barrow.
Leicester: J Liley; S Hackney, S Potter, W Greenwood, L Lloyd; R Liley, A Healey; G Rowntree (P Freshwater 32-37), D West, D Garforth, M Johnson, N Fletcher, J Wells, N Back, D Richards (capt).
Referee: S Piercy (Goole).
n Selected top-flight matches in Wales look likely to go ahead this weekend despite referees' strike action over pay, but there could still be a greatly reduced programme. The Welsh Rugby Union has offered to pay referees in charge of matches in the top two divisions, but the officials want payment for taking charge of fixtures for all five divisions. Referees will only definitely be provided for 12 games this Saturday, including six Swalec Cup fifth-round ties.