Australia reached 330-2 in 81.1 overs when rain stopped play for the day after the tourists elected to bat first in Galle at the start of the two-match series.
Left-handed opener Khawaja, on 147, and skipper Smith put on an unbeaten stand of 195 to thwart the opposition attack in two wicketless afternoon sessions.
“We have played a lot of cricket in the sub-continent but not been able to put pressure on the opposition. But today, we definitely did that,” Khawaja said.
He added, “Showed how fast we were scoring until they tried to bowl a bit negative line after tea.”
Milestone man Smith got three runs off spinner Nishan Peiris to reach his third ton in four matches as he took off his baggy green and raised his bat to acknowledge the crowd’s cheers.
Smith took the crease in the first session with 9,999 runs and calmly nudged his very first delivery to mid-on for a single off Prabath Jayasuriya.
He became the 15th batsman to 10,000 Test runs and only the fourth Australian to achieve the feat after Allan Border, Steve Waugh and Ricky Ponting.
Smith survived an early reprieve in his knock when Jayasuriya grassed a sharp return catch in the same over, a chance Sri Lanka would come to rue.
He made the hosts pay dearly, crafting a sublime 35th Test century to reaffirm his stature as one of Australia’s rock in the middle-order.
Khawaja reached his 16th Test hundred — his maiden ton on Sri Lankan soil — after a 17-match drought since his Ashes century in June 2023.
The ton came with a flick off fast bowler Asitha Fernando to the fine leg boundary, a stroke brimming with elegance and relief.
The 38-year-old had a few heart-in-mouth moments when a couple of edges fell just short of fielders and a reprieve on 74 when he nicked Jayasuriya to the keeper, but Sri Lanka chose not to review the on-field decision.
Another opportunity slipped through Sri Lanka’s fingers with Smith on 90 as Kusal Mendis, slow to react behind the stumps, spilled a bat-pad chance. Earlier, Travis Head smashed 57 off 40 balls including 10 fours and one six to put Sri Lanka on the back foot right away.
“The wicket is not a usual Galle wicket. It’s on the slow side,” Sri Lanka’s spin bowling coach Piyal Wijetunga told reporters.
“When the wicket is not helping the bowlers, you should try to show more discipline and I don’t think we bowled well today.”
Head, who replaced 19-year-old Sam Konstas as an opener for the Test, put on 92 runs with fellow left-hander Khawaja. The hosts finally found a breakthrough when Head misfired an ambitious charge against Jayasuriya only to find the long-on fielder.
Jeffrey Vandersay had Marnus Labuschagne caught at first slip for 20 with his left-arm spin. With three specialist spinners in the Australian XI, the tourists hold all the aces, especially with the pitch expected to deteriorate as the game progresses.