Heazlett's unbeaten 118 ensured the Bulls held off SA's push for victory on Sunday's final day of play.
The 23-year-old left-hander batted through the entire day to anchor Queensland's 6-357 in their second innings, a lead of 83 runs when stumps were called early, with no result other than a draw possible.
Heazlett, Charlie Hemphrey (87) and Michael Neser (57no) stubbornly resisted SA's bowlers, who could muster just three wickets on the last day.
Pacemen Chadd Sayers and Joe Mennie claimed three victims each for the innings but teenage leg-spinner Lloyd Pope was wicketless.
After becoming the youngest bowler to take seven wickets in a Shield innings in Queensland's first innings, Pope finished with 0-101 from 34 overs in the second dig.
Heazlett produced a stellar knock, facing 356 balls and featuring in two defining partnerships.
He put on 118 runs for the fourth wicket with Hemphrey, and then combined with Neser for an unbroken 93-run union for the seventh wicket.