Kumar Sangakkara made 55 for Sri Lanka, which is preparing for the first of three tests against Australia beginning next Friday in Hobart.
Earlier, Chairman's XI opener Scott Henry completed his unbeaten double century before the hosts declared their first innings on 439-6 after 100 overs, as per the rules.
Dhammika Prasad, who endured a tough time bowling Thursday, picked up the wickets of Travis Head (35) and Sam Whiteman (4) to finish as the only multiple wicket-taker for Sri Lanka with 2-128.
The Chairman's XI claimed three early wickets, split evenly between young West Australian offspinner Ashton Turner, Victorian allrounder Glenn Maxwell and captain Usman Khawaja.
West Australian offspinner Ashton Turner (1-54) made the first breakthrough for the Chairman's XI, ending the 105-run opening partnership when he had Dimuth Karunaratne caught at mid-on by Marcus Harris for 40.
Sangakkara was in good touch before captain and part-time bowler Usman Khawaja (1-22) trapped him lbw.
Dilshan retired at tea to give other batsmen some time at the crease ahead of the test series.
Wicketkeeper-batsman Prassana Jayawardene added an unbeaten 24 while Dinesh Chandimal is 12 not out.
Sri Lanka rested four of its big names, including Angelo Mathews, star spinner Rangana Herath and middle-order batsman Thilan Samaraweera.
Chairman's XI 439-6 dec. (Scott Henry 207 not out, Glenn Maxwell 91; Dhammika Prasad 2-128). Sri Lanka 276-4 (Tillakaratne Dilshan 101 retired, Kumar Sangakkara 55; Usman Khawaja 1-22).
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