"This will be a pressure match for all of us," Mathews said of the Pool A encounter at the iconic Melbourne Cricket Ground.
"It will certainly be a tough game. Bangladesh have performed well in the recent past. They have a good set of players and we have to take all their batsmen and bowlers seriously.
"Whoever plays the best cricket will win and we hope we can play our best cricket tomorrow."
Bangladesh were hammered by 10 wickets in 2003 and by 198 runs four years later in the teams' only two previous World Cup meetings, leaving Sri Lanka overwhelming favourites to extend the streak.
But Mathews' men have had an uninspiring start to the 2015 event, with their batsmen struggling to cope with conditions in New Zealand.
Sri Lanka were thrashed by the co-hosts in the tournament opener in Christchurch, going down by 98 runs after New Zealand had piled up 331 for six.
Having left New Zealand with two points from as many games, Sri Lanka will hope the change in scenery and conditions in Australia will galvanise their campaign.
