Australia went to lunch at 6-201 on Saturday, with a lead of 374 and five sessions still to play at The Oval.
Runs were hard to come by on the fourth morning, with Australia adding 78 to their overnight score after losing Marnus Labuschagne for 41 in the third over of the day.
But what will please Australia is the patience with which Carey (41no) and Cameron Green batted, six days out from the first Ashes Test against England at Edgbaston.
Both were watchful throughout the opening session in a 43-run sixth-wicket stand, before Green was bowled by Ravindra Jadeja trying to leave on 25.
Green soaked up 95 balls in his innings, as he readjusted to Test cricket mode after arriving in England following two months in the hurry-scurry of the Indian Premier League.
The allrounder wore one blow to the shoulder that required attention from medical staff, but largely gutsed it out against India’s quicks.
He was out in the first innings driving at a ball well away from his body, but was far more composed in the second.
With his feet moving well, he played the shot of the morning when he sent a Mohammed Shami ball back past the Indian quick for four.
But he eventually became tied in a web by Jadeja, bowled when a ball bounced off his gloves and onto the stumps after he attempted to shoulder arms to the spinner.
Carey was also watchful.
The wicketkeeper has seemingly put the risky reverse sweep to bed when facing India spinner Jadeja (3-45), after being dismissed four times on the shot this year.
Instead, he nurdled the ball around against the spinner, scoring his runs through the offside from the quicks with several neat cover drives and cut shots.
He came to the wicket after Labuschagne edged a Umesh Yadav ball that seamed away slightly, leaving the Queenslander caught at slip.
Australia’s lead means India will already need to break a record for the biggest fourth-innings chase at The Oval to win the match, with the previous mark of 263 set by England in 1902.