Worcester closed the gap to just six points on 11th-placed Northampton with a 10-9 success at Franklin's Gardens on New Year's Day.
And Warriors' vastly-improved defensive organisation - they have conceded only nine tries in their last seven matches - continues to underpin hopes of avoiding the drop.
Former England defence coach Phil Larder has made a considerable impact since arriving at Sixways, although Drahm accepts Wasps, who need one try for their 600th in Premiership history, will pose threats all over the Adams Park pitch.
"We have been working on our defence, and that has really showed," said the Australian, who lines up at full-back tomorrow.
"We haven't given away many tries in the past few weeks. Credit to Phil Larder. He is a great guy to have around - he's given us confidence in defending.
"But it is very hard to win at Wasps. They have seven backs who are all dangerous, yet with our defence working the way it is, and us cutting out a lot of our penalties, it will probably be a tight one.
"Obviously, we are looking to win every game. If we can get another two wins in the next three or four games, that will give us a lot of confidence and put us where we want to be."
Warriors rugby director John Brain makes four changes from the side that edged out Northampton, calling up scrum-half Matt Powell, prop Darren Morris, hooker Chris Fortey and number eight Kai Horstmann, while newly-appointed England captain Phil Vickery returns for Wasps after missing the defeat against Bath five days ago.
Wasps also include teenagers Danny Cipriani and Dominic Waldouck in their back division, and rugby director Ian McGeechan said: "We are continuing to develop our young talent, giving the players the opportunity to gain experience in important games on the big stage."
Bristol captain Matt Salter makes his first start since suffering a dislocated shoulder in mid-October when the Premiership leaders host Northampton tomorrow.
Salter replaces injured flanker Joe El Abd, who was injured in the win against champions Sale Sharks on New Year's Day, while Bristol's England scrum-half Shaun Perry remains sidelined because of a rib problem.
Wing Ben Cohen, who failed to gain a place in England's RBS 6 Nations squad earlier this week, lines up at outside centre for Saints' west country trip.