The reigning champions, chasing an unprecedented third successive title, have gone 25 games unbeaten at the World Cup since losing to Pakistan at Headingley eight years ago, a sequence that includes their famous tied semi-final against South Africa in 1999.
Australia's nine-wicket thrashing of Ireland on Friday was their 19th straight World Cup win and meant they became the first team in the Caribbean to qualify for the semi-finals.
New Zealand and Sri Lanka have also joined them in the last four courtesy of the Black Caps' win over South Africa on Saturday.
"I think we have a very good record against Australia," said Jayawardene. "Why? Because we play our brand of cricket and we are not afraid of doing that."
But Sri Lanka will still be without Lasith Malinga who has an ankle injury.
The 23-year-old, whose unorthodox action makes him difficult for batsmen to pick up, hasn't played against Australia and Jayawardene admitted there was a case for keeping him 'hidden' until a possible meeting with Ricky Ponting's side in either the semi-finals or final.
"That's one way to look at it but there are so many other ways to look at it."
Jayawardene also said it was vital the likes of 1996 World Cup winning bowlers Chaminda Vaas and Muttiah Muralitharan maintained their recent form.
"Australia are getting good starts and there hasn't been that much emphasis on their middle order so that's one area we'll be thinking about," he explained. "They've got a good balanced bowling attack as well."
Sri Lanka's last one-day win against Australia, in Adelaide in February 2006 saw Tillakaratne Dilshan involved in four run-outs of home batsmen.
And Jayawardene praised the off-spinning all-rounder as one of the "dirty work" players all successful sides needed.
"Most of the teams do have that all-rounder in their side who does all the dirty work for you, gets that 30 or 40 runs, bowls five or six overs, gets you one or two wickets and probably pick up a half-chance or a run-out."
Meanwhile, Australia quick Glenn McGrath said opener Sanath Jayasuriya, whose dynamic batting played a major role in Sri Lanka's World Cup triumph 11 years ago, was a key target.
"There is no doubt he is a great player and we'd like to get on top of him early and knock him over," said McGrath, on the losing side in the 1996 final.
"From what we've seen, the pitch in Grenada is slower and takes some turn. It will be a big test for us and probably suit Sri Lanka."
McGrath, the World Cup's leading bowler of all-time with 63 wickets, said that Australia's lack of a close game in the Caribbean wouldn't be an issue as the World Cup neared its conclusion.
And the 37-year-old, due to retire after the tournament, insisted now was the time when players such as himself and fellow two-time World Cup winners Ponting and Adam Gilchrist would come into their own.
"The next two weeks for us is the showcase time for the whole tournament, and our senior players, who have been in World Cups before, I think that's when you'll see them stand up and start enjoying the tournament for what it is."