The Middlesex left-hander hit 63 in a disciplined 128- ball innings before a rare rush of blood cost him his wicket, attempting to cut through point only to be caught at slip in the final over of the pink ball day/night match.
But Malan has probably done enough to cement his place at number five for the Ashes opener in Brisbane later this month after his second half-century in consecutive innings.
"Some of the dismissals we had today were a touch on the sloppy side, so it was a little bit frustrating more than anything that we didn't kick on and probably have a couple of hundreds scored out there today," Stoneman said.
"Everyone got a bit of time in the middle, so that was encouraging, but we also need to be scoring hundreds, and big hundreds.
"So there are lessons to be learnt from today."
Malan helped revive the innings after the tourists had slumped to 195 for five following Jonny Bairstow's dismissal for nine in the 62nd over.
Malan put on 76 for the sixth wicket before Chris Woakes fell for 33.
A total of four wickets fell in the final night session of play at the Adelaide Oval, where the first day-night Ashes Test takes place next month.
Young New South Wales leg-spinner Daniel Fallins, in his maiden first-class match, rocked the tourists with the wickets of Stoneman, James Vince (33), Root and Bairstow to finish the day with four for 71 off 21 overs.
"I was quite nervous last night, but getting a wicket in my first over really settled the nerves and the boys really got around me, so that was good," Fallins said.
Cook's lean start to the tour continued when he was again dismissed cheaply, in the seventh over.
After a second-ball duck in England's tour opener last week against a Western Australian XI in Perth, Cook faced only 28 balls.
He was dismissed when feathering an outside edge from an attempted forward defensive shot off paceman Jackson Coleman.
Vince was bowled by Fallins when attempting a sweep shot from the spinner's fifth ball and Stoneman fell to a brilliant one-handed diving catch at mid-wicket by Jake Carder.
And just before the dinner break, Fallins claimed Root when the skipper top-edged a front-foot swipe and was caught by Ryan Gibson at mid-off.
England, who have lost paceman Steve Finn for the tour with a knee injury, rested strike bowler Stuart Broad.
Following the Adelaide game, they have another four-day fixture against a CA XI in Townsville from November 15, before the first Test against Australia starts on November 23 in Brisbane.
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