Patterson scored an unbeaten 102 in the second innings on day three, following up his 157 not out in the first innings.
Sri Lanka declared on 176/5 in 75 overs against the pink ball in Hobart.
Mendis left the field immediately and spent the rest of the day icing the injury to his right ring finger.
Patterson and Doran put on 218 for the sixth wicket at Blundstone Arena.
Burns, Labuschagne and Renshaw were dismissed inside 11 overs in Hobart.
Cricket Australia XI wicket-keeper batsman Harry Nielsen expressed his happiness after his side managed to frustrate India with a mammoth batting effort during the sole tour match ahead of the first Test next week.
Murali Vijay hit a stylish century Saturday to strengthen his bid to open the batting in the first Test against Australia, after India's rusty bowlers struggled against a young CA XI
The 19-year-old pacer finished the day with 4/50 in his 13 overs as the visitors were bowled out for 358.
Prithvi Shaw began his maiden tour Down Under clobbering 11 fours en route to his 69-ball 66-run knock.
Bangar said Rahul was no longer an inexperienced player and he ought to shoulder more responsibility.