Eighteen-year old Sangha and team skipper Short -- with only seven first-class matches between them -- shared in a 263-run fourth-wicket stand to draw the four-day game ahead of next week's first Brisbane Test.
Sangha hit 133 off 226 balls with 13 fours and a six, while Short remained unbeaten on 134 off 264 balls when the game was called off late on the final day in Townsville.
Sangha is the second youngest player to score a century against England behind India great Sachin Tendulkar.
He was finally caught off leg-spinner Mason Crane, allowing the tourists to avoid the indignity of going wicketless on the final day.
The inexperienced CA XI finished on 364 for four off 110 overs to lead by 99 runs when the rival captains agreed a draw.
Sangha was dropped by Mark Stoneman on 43 but England's bowlers created few other chances.
England comfortably defeated a similar CA XI in Adelaide last week and for two days in north Queensland they had looked set to do so again.
The CA XI ended the third day on 121 for three, trailing England by 144 and short of a batsman because of an injury to Nick Larkin.
But Sangha and Short made the most of the benign conditions to ensure England spent the fourth day toiling in the tropical heat.
Pace bowler Craig Overton was treated with disdain, going wicketless for 65 off 15 overs.
Off-spinner Moeen Ali, in his first game of the tour after a side injury, bowled a total of 48 overs in the match. But fellow spinner Crane was loose, finishing the second innings with two for 97 from 30 overs.
By the end, England were using part-time spinners Joe Root and Dawid Malan to protect the frontliners and hasten the finish.
First Published: November 18, 2017, 1:05 PM IST