The Welsh region's chances of qualifying for the knockout stages are remote since defeats by Leinster and Northampton left them bottom of Pool One.
Wales stars Alun Wyn Jones, Dan Biggar, Justin Tipuric and Ryan Jones have been named in the starting XV but hooker Richard Hibbard has been left on the bench.
"We do believe we can win. On the day anything can happen and we go there more than confident because we have some guys who are playing very well," Ryan Jones said.
"We're facing arguably one of the best teams in Europe and we'll give it everything we've got.
"This is what Heineken Cup rugby is all about. It's what guys thrive on - going to the best teams with the best individuals. We'll throw the dice and see how it goes."
Prop Adam Jones is out with a calf problem and lock Ian Evans is to remain at home as his partner is soon to give birth.
British and Irish Lions duo Leigh Halfpenny and Alex Cuthbert return for Cardiff Blues as they seek to build on their victory over Toulon by toppling Glasgow at the Arms Park tonight.
Only one point separates leaders Exeter from bottom-placed Cardiff, who blew Pool Two wide open by stunning reigning European champions Toulon 19-15 in October.
"The next two weeks will go a long way to deciding our fate in the Heineken Cup," Blues director of rugby Phil Davies said.
"It's vital we start strongly and get another crucial victory at the Arms Park.
"Our win over Toulon will always live long in the memory. It was a famous day for our region.
"Now it is vital we build on that result because the pool is wide open after two games and every team is chasing top spot."
Glasgow skipper Al Kellock will make his 50th Heineken Cup appearance in the first match of a double header that head coach Gregor Townsend views as key to the Warriors' quarter-final aspirations.
"We know the outcome of these games will be pivotal to our hopes of progressing in the tournament," Townsend said.