Thirimanne, who only arrived in Australia this week to cover for the injured Kumar Sangakkara, threw away a chance of a first Test hundred.
Jayawardene scored his first away Test 50 in more than three years but was caught at slip on 72.
Earlier, the skipper Mahela Jayawardene led from the front with 72 after being sent in to bat by the home side, who lead 2-0 in the three-Test series.
The last time Jayawardene had passed 50 outside Sri Lanka was way back in November 2009 in India, although he has continued to score heavily at home. He went 26 innings outside Sri Lanka without a half-century.
At the interval Lahiru Thirimanne, who only arrived in Australia this week to cover for the injured Kumar Sangakkara, was on 37 not out after having a leg before wicket dismissal overturned on review on the first ball he faced.
After his close shave Thirimanne knuckled down to play straight and add some solidity to the Sri Lanka batting, woefully missing in Melbourne last week where they lost by an innings and 201 runs after being routed for 103.
Australia removed both Sri Lankan openers in the morning session.
Skipper Michael Clarke looked for a quick return on a bold decision to bowl after going into a Test with four quicks for the first time since the third Test against India in Perth a year ago.
Jackson Bird snared the wicket of Dimuth Karunaratne in the eighth over but Australia had to wait until 20 minutes before lunch for a second, with the dismissal of Tillakaratne Dilshan.
Karunaratne was out to a poor shot, attempting to pull Bird but only getting a top edge that was safely caught by Mike Hussey, playing in his 79th and last Test match. Dilshan was caught behind off Bird for 34. Veteran Jayawardene was under pressure to perform in the absence of veteran Sangakkara, who suffered a fractured finger while batting in Melbourne.
The Sydney Test had a poignant opening with Australian and Sri Lankan players paying their respects to Tony Greig in a moving farewell to the former England captain.
Players and fans observed a minute’s silence in honour of Greig, who died at the weekend aged 66 from a heart attack while battling lung cancer.
Brief Scores: Sri Lanka 294 (Lahiru Thirimanne 91, Mahela Jayawardene 72; Jackson Bird 4 for 41, Mitchell Starc 3 for 71) vs Australia