After his side won the toss against Queensland, opener McInerney (142 off 222 balls) powered the hosts to 4-359 at stumps at Karen Rolton Oval - the same venue where they will be forced to host the final following a controversial intervention from the AFL.
McInerney, 30, almost doubled his previous first-class high score of 75 with 23 fours on a scorching hot day in Adelaide.
Queensland played seven different bowlers in short spells to combat the heat, and the strategy paid off as Marnus Labuschagne (1-29) finally had McInerney's big wicket with his part-time pace.
McInerney skied Labuschagne's bouncer to short extra cover where he took a catch from his own bowling, celebrating as jubilantly as one would expect from the energetic Test No.3.
Former Test opener and South Australia captain Nathan McSweeney (41) had found himself caught on a similarly loping shot, edging Jack Wildermuth (1-49) to midwicket earlier in the day.
Jason Sangha (67) made a valuable half-century before being trapped lbw by two-time Test quick Michael Neser (1-54)
Alex Carey (46no from 50 balls) is unbeaten at the crease alongside son-of-a-gun Jake Lehmann (27no from 31 balls) after some positive ball-striking from the Test wicketkeeper later in the day.
Carey memorably pulled Wildermuth over cover for the innings' only six so far.
Adelaide, which reported temperatures around 40 degrees on Saturday, is expected to cool down for day two as Queensland chase quick wickets to wrestle control back.
29°C