Worcester head into the weekend just one point ahead of the Premiership's bottom side Northampton, who are in action against Newcastle at Kingston Park on Sunday.
They lifted themselves off the bottom with consecutive victories over Sale and Newcastle and Brain has urged them to continue that form at Sixways.
"We are playing well and we have got to make sure we are keen to get going again. The start to the game will be crucial and that is the key to re-establishing some momentum," he said.
"We know if we approach the game in the right way we are in with a real shout of winning it.
"It is close at the bottom. This is effectively another cup final."
Captain Pat Sanderson is back in action after recovering from a broken hand and the Warriors front row is bolstered by the return of Wales prop Chris Horsman.
But Worcester face a Bristol side with the chance to cement their play-off credentials.
Bristol head into the weekend just a point behind third-placed Saracens and four ahead of Wasps, with the two London clubs meeting on Sunday.
Bristol boss Richard Hill said: "I know John Brain well and I imagine he'll have his forwards stoked up for one big effort. This is a game that they've probably targeted having looked at our last few results.
"We've got just as big an incentive given that our last two games will be against Gloucester and Leicester. We're at home and we need to win and, with Saracens playing Wasps this weekend, a win would help put some daylight between ourselves and one of them."
Gloucester can press on for a top-two finish - and the bonus of a home Premiership semi-final - with a win over west country rivals Bath.
The Cherry and Whites have full-back Iain Balshaw and Mike Tindall back in the side and featuring against their old club.
Bath welcome back England hooker Lee Mears as the only change from last weekend's comprehensive European Challenge Cup win over Bristol.
Next season's European competition remains up in the air following the Anglo-French boycott - but that does not mean London Irish will take their foot off the pedal.
The Exiles tackle a Harlequins side featuring former New Zealand fly-half Andrew Mehrtens and boss Brian Smith said: "We want to win to ensure we finish in the top half of the table and position ourselves for qualification for whatever form of European competition may emerge from the current discussions."