The sixth wicket stand between Pup and Hopes (34) fetched a brisk 63 runs to help Australia reach a competitive 253/6.
Clarke top-scored with workmanlike 77*. Gilchrist made an untypical 81-ball 61 and Hayden a solid 42.
Clarke held his ground firm at one end as wickets tumbled at the other end. He hit just two fours and a six in his patient 86-ball innings but his stands with Gilly, Hussey and Hopes in the fag end rescued Aussies.
The tourists struck at regular intervals on a slowish wicket, forcing Aussies to build the innings rather than blast away against a probing attack.
Ever reliable Vaas was the pick among Lankans bowlers with 2 for 34 in his quota of 10 overs while rookie seamer Amerasinghe, who bowled to a tidy line and length in his initial spells, leaked a plenty in the later spell for his 2/66.
The Lankans suffered a scare late in the innings when spinner Muttiah Muralidaran took a blow in the face after stumbling in the field.
The tourists will fancy their chances of roping in Australia's tally, especially if the top order gets going in the evening session.
Earlier, openers Gilchrist and Hayden got off Aussies to a solid start with 65-run stand in less then 13 overs. Hayden made a strokeful 42 studded with five boundary hits before edging rookie seamer Amerasinghe for a regulation slip catch. Ponting came and went in whimper to leave Australia reeling on 88/2.
Clarke joined Gilchrist in the middle and steadied innings with 51-run stand. Gilly in his last series played an untypical dogged innings and looked determined to make a big score was undone by a straigter one that rapped Gilly on off and middle stump line.
The retiring keeper-batsman swung across the line and was given out LBW after a long deliberation by the umpire. A subdued Gilchrist hit just three boundaries in his 81-ball stay.
Andrew Symonds (12) never really got going and was the next batsman out, blasting a catch to Kapugedera at extra cover off Vaas.
Mike Hussey joined Clarke at the crease and the pair began working the ones and twos before the Western Australian threw his wicket away on 10.
Walking down the pitch, Hussey cut Amerasinghe straight to Dilshan at backward point.
It left Australia in a spot of bother at 190/5 in the 42nd over, but Hopes and Clarke avoided further damage.
Hopes was out in the final over, spooning a catch to Dilshan at backward point after an invaluable 29-ball knock.
Australia 253/6 in 50 overs (Clarke 77 n o, Gilchrist 61, Hayden 42, Hopes 34; Vaas 2 for 34, Amerasinghe 2 for 66) Vs Sri Lanka.