The pair, who came together in the first over after lunch with the tourists struggling at 59 for two, defied Australia until the close of play on the fourth day at the Gabba.
England, chasing a victory target of 508, reached 211 for two at the close -- and now need 297, with eight wickets standing, for an improbable victory.
Although an England win is still possible, Mike Atherton's side faces the more realistic challenge of batting through the final day to earn a draw.
Hick, who ended the day on 72, and Thorpe, not out 66, displayed tremendous resolve and concentration in adding 152 runs during a stand which lasted three balls short of two sessions.
It was England's highest test partnership at the Gabba, eclipsing the 124 that Bill Edrich and Peter May put together in 1954-55.
Australia captain Mark Taylor, who surprisingly opted not to enforce the follow-on Sunday, repeatedly shuffled his attack without success.
Indeed, the Australian bowlers, so dominant until Thorpe and Hick came together, showed increasing frustration as the day wore on.
Leg-spinner Shane Warne, who grabbed the wickets of openers Alec Stewart and Atherton, was the only bowler who looked capable of breaking through.
Warne broke England's first wicket partnership with the total on 50 when he bowled Alec Stewart for 33.
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