The game proved a sloppy, error-strewn contest, but although Bristol have now gone five matches without a league win stretching back to late December, two hard-earned points lifted them seven above basement club Leeds.
Two Tommy Hayes penalties and a second-half Jason Strange strike kept Bristol in the hunt against a subdued Wasps outfit, for whom Mark Van Gisbergen slotted two penalties and fly-half Jeremy Staunton kicked one.
Try-scoring chances were at a premium, while a bruising encounter took its toll on England men Lawrence Dallaglio and Tom Voyce ahead of next Saturday’s Calcutta Cup appointment with Scotland at Murrayfield.
Wasps skipper Dallaglio played the second-half with a bandage on his hand, while a bloodied Voyce did not return after going off on 58 minutes.
Wasps are now eight points behind league leaders Sale Sharks, but their title play-off spot looks assured, while Bristol face a vital away clash against fellow strugglers Saracens next Sunday.
Bristol handed a first league start to former Worcester fly-half Hayes, while back-row changes saw flanker Craig Short and number eight Dan Ward-Smith called up.
Wasps were without England full-back Josh Lewsey as he continued his recoveryfrom a shoulder injury sustained during the RBS 6 Nations Championship victory over Wales two weeks ago, and Staunton took over from injured fly-half Alex King.
Elsewhere, England flanker Joe Worsley was rested as Dallaglio’s team targeted a victory that would consolidate second place.
Hayes, who endured an uncertain start with his tactical kicking, booted Bristol into a third-minute lead, but Van Gisbergen cancelled out the advantage four minutes later before Wasps lost centre Stuart Abbott because of an ankle injury.
Abbott’s departure meant an 11th-minute introduction for Ayoola Erinle, and as Hayes gradually grew in confidence, so Bristol gained a foothold in the game.
Wasps’ early promise was countered by an aggressive Bristol pack that built the platform for Hayes’ second successful penalty, on 20 minutes.
Bristol deserved their narrow advantage, but Hayes then drifted a 40-metre kick wide after Dallaglio was penalised for a high tackle on home scrum-half Shaun Perry.
Dallaglio required treatment on his hand shortly afterwards, yet he would have been more pained by Wasps’ performance, despite Van Gisbergen’s equalising second penalty just before half-time.
Van Gisbergen was wide of the target with another penalty during eight minutes of first-half stoppage time. Wasps though, inched ahead when Staunton took over kicking duties and made it 9-6 to end a scrappy opening period.
Dallaglio returned after the break with the fingers on his right hand strapped, and Wasps continued their struggle for fluency, confirmed when rugby director Ian McGeechan made three substitutions by the 55th minute, sending on prop Justin Va’a, hooker Ben Gotting and flanker Jonny O’Connor.
Bristol boss Richard Hill also sought greater impetus, replacing the erratic Hayes with Strange, Bristol’s top points scorer this season.
Frustration became increasingly evident on both sides, and Wasps centre Rob Hoadley was involved in a wrestling match after the visitors’ defence only just prevented Bristol wing Lee Robinson touching down wide out.
Wasps wing Voyce was hurt following his part in the Wasps rearguard, and he left the action for treatment to a cut mouth as Fraser Waters replaced him.
Strange slotted a short-range penalty to level the game, and Bristol continued on the front foot, helped by Perry’s 60-metre touchfinder after Wasps lock Simon Shaw’s deft pass to Waters almost opened up the home defence.
Bristol’s forwards, inspired by number eight Ward-Smith, battled on in pursuit of a territorial foothold, and with Wasps offering little in response, a priceless home victory remained the most likely outcome.
Staunton though, missed a straightforward penalty chance three minutes from time after a rare Wasps attack, and in a game containing so few clear-cut scoring opportunities, his body language told its own story.
The excellent Perry then took Bristol back into Wasps’ 22 through another teasing kick, yet the stalemate could not be broken, leaving Wasps to reflect on their second successive Premiership draw and Bristol claiming a priceless two points.