The Bulls were all out for 445 in their second innings, a lead of 269 runs, on the stroke of stumps on day three of the Shield decider in Adelaide.
The highest run chase to win a Shield final is Victoria's 2-239 against NSW in 1990/91.
Clayton and Wildermuth struck contrasting but equally crucial centuries in a remarkable revival of Queensland's fortunes on Friday at Karen Rolton Oval.
Clayton's plucky 100 from 249 balls was followed by Wildermuth's free-flowing 111 from 140 deliveries.
Queensland had been on the ropes since being bowled out for 95 in their first innings, with a Jake Lehmann century steering SA to 271 all out in reply.
And the Bulls' chances appeared remote on Friday when at 6-221, just 45 runs ahead, when Clayton and Wildermuth were united.
The pair turned the tide with a 103-run partnership, defying an SA attack led by ex-Queenslander Brendan Doggett who has returned the best match bowling figures in a Shield final.
Doggett followed his 6-31 in the first innings with 5-109 for a combined 11-140. Tasmania's Shane Jurgensen (11-172 in 2001-02) is the only other bowler to take as many wickets in a Shield decider.
Clayton, who ran himself out for a golden duck in the first innings, reached his fifth first-class ton from 247 balls.
Two balls later, the left-hander was trapped lbw by spinner Ben Manenti (1-38).
Wildermuth, who went eight years between Shield centuries but has now scored two in two games, hammered SA's bowlers in a knock featuring 18 fours.
The 31-year-old found another ally in No.9 Mark Steketee, who made 51 and posted a match-high 122-run stand with Wildermuth, who was bowled by Nathan McAndrew (3-106) about 30 minutes before stumps.
The Queenslanders are eyeing their first Shield title since 2020-21 while trying to extend SA's drought which dates back to 1995-96.
But the South Australians are hoping to collect the Shield and the one-day trophy in the same season for the first time, after their victory in the 50-over final against Victoria on March 1.
20°C