Jaques, who was recalled following the retirement of the regular opener Justin Langer, crafted a fine 100 before being dismissed by Murali.
Matthew Hayden (43) and Ricky Ponting (56) also producing good contributions as Australia reached 242-3.
Muralitharan bowled menacingly, taking 2 for 67 to stand six wickets shy of Shane Warne's Test record of 708.
He had the prized scalps of Jaques and Ponting stumped and was unlucky not to take more wickets. Jaques was first spilled on 60 - Jayawardene the offender - and than Thilan Samaraweera repeated the mistake when the batsman had reached 90.
Sri Lanka spilled four catches during the course of the day - and caused Michael Hussey plenty of problems late in the day.
After winning the toss, the tourists surprisingly put Australia in to bat on a batting strip - a decision echoing Nasser Hussain's infamous error of 2000.
The tourists had left out their fastest weapon Lasith Malinga - with Chaminda Vaas and Farveez Maharoof doning the new-ball bowler roles.
Injured Kumar Sangakkara failed fitness test, leaving a hole in the Sri Lanka batting.
Jaques took 34 balls to get off the mark but took advantage of the numerous loose balls that came after lunch, feasting on some wayward short-pitched bowling from Dilhara Fernando.
Hayden was typically more confident, walking towards the bowlers and finding boundaries with powerful cuts and drives.
He departed for 43, however, with the scoreboard on 69 in the 23rd over, when he tried to drive Vaas over the bowler's head, only to sky the ball wide of Muralitharan at mid-off.
The fielder sprinted to his right to take an excellent catch.
Jaques then put on 114 with Ponting, who quickly found his touch by feasting on the inconsistent Fernando.
But soon after tea, the Australia skipper was drawn forward by a Muralitharan 'doosra' delivered from around the wicket and Prasanna Jayawardene did the rest.
The New South Welshman constructed his innings patiently. He earned his first Test century cutting Vaas to the cover boundary.
Moments later, he charged Murali only to misread a heavily-spun off-break, and was easily stumped.
Hussey (5*) and Michael Clarke (28*) took Australia to stumps, though Hussey was dropped at midwicket on 13 by Marvan Atapattu off Maharoof.
Brief Scores (D-1):
Australia Ist innings 242 for 3 (Jaques 100, Ponting 56, Hayden 43; Muralitharan 2 for 67, Vaas 1 for 44) Vs Sri Lanka.
ThatsCricket (with inputs from BBC)