Khawaja (166 not out) brought up his sixth Test century in the first session and he built on that on a flat SCG pitch Saturday.
He was joined by Shaun Marsh (unbeaten 54), with the duo putting on an unbroken 91 for the fourth wicket as Australia pushed to 365-3 at tea, a lead of 19 runs.
Moeen Ali (1-98), Mason Crane (0-93) and Joe Root (0-12) have found some turn, but not enough to seriously trouble Australia.
Root thought he had Marsh when the left-hander was given out caught behind on 22.
However, the Australia batsman reviewed and replays showed he hit his pad – not the ball.
That was as close as England came to a breakthrough in the middle session, during which the hosts scored 88 runs.
The pitch is expected to deteriorate, but day three has so far proven to be a good one for batting in warm conditions.
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