Leicester's Hipkiss was named man-of-the-match against Bristol
Leicester: (20) 26
Tries: Ellis, Murphy
Cons: Goode (2)
Pens: Goode (4)
Bristol: (9) 14
Pens: Gray (3)
Leicester ground down Bristol with a controlled, intelligent and powerful display in the Premiership semi-final to keep alive their treble hopes.
The Tigers reached their third straight Premiership final with tries from Harry Ellis and Geordan Murphy, while Andy Goode kicked 16 points.
Bristol's only try came through Sam Cox, with Danny Gray kicking their other points.
Leicester will meet Gloucester in the final at Twickenham on 12 May.
The Tigers, beaten Premiership finalists in 2005 and 2006, lifted the EDF Energy Cup last month and will also take on Wasps in the Heineken Cup final on 20 May.
Long-time league leaders Bristol began in lively fashion and went ahead with a penalty from Gray but Leicester surged clear when Ellis picked up from the back of a rolling maul and scampered over on 10 minutes.
Goode added the extras and followed it up with a quick penalty, before trading three-pointers with Gray.
Bristol kept themselves in the game with another penalty but Tigers opened the first meaningful gap when Murphy burrowed over following a period of sustained pressure.
Tigers went in at the break leading 20-9 but Bristol struck back quickly on the resumption when Gray fed a clever inside ball for Cox to scythe over.
Bristol threatened to edge their way back into the match but two penalties from Goode kept the visitors at arms length.
Both sides lost players to the sin-bin inside the last quarter - first Joe El Abd for Bristol and then Alesana Tuilagi for Leicester.
But it was the experience and determination of the Leicester pack that set up the Twickenham clash between the league's top-two finishing sides this year.
Leicester: G Murphy, Rabeni, Hipkiss, Vesty, Varndell, Goode, Ellis; Ayerza, Chuter, Moreno, Deacon, Cullen, Moody, Jennings, Corry (c).
Replacements: Buckland, White, Kay, Deacon, F Murphy, Smith, Tuilagi
Bristol: Arscott, Robinson, Brew, Cox, Lemi, Gray, Perry, Hilton, Regan, Crompton, Winters, Llewellyn (c), Budgett, El Abd, To'oala.
Replacements: Linklater, Clarke, Hohneck, Short, Nicholls, Hill, Morgan