Chasing 362 for victory in a minimum of 62 overs, Queensland finished at 1-120 off 35 overs before the captain's shook hands at 4.22pm local time at the WACA Ground on Friday.
Bulls veteran Usman Khawaja scored 64 not out and Marnus Labuschagne 35no, but opener Matt Renshaw (15) was caught behind off the bowling of Matt Kelly.
It followed on from Renshaw's dismissal for six in the first innings, dealing a blow to his hopes of earning a Test recall.
WA opener Cameron Bancroft also harmed his Test chances with a pair of ducks.
The news was better for Marsh, who produced a solid knock in WA's second innings total of 6-263 declared in a good warm-up for the five-Test series against India.
Marsh (94 off 142 balls) struck 14 fours and one six to put himself within one mighty blow of bringing up three figures.
But his attempted pull for six off the bowling of Jack Wildermuth (3-38) skied into the air, with wicketkeeper Jimmy Peirson taking an easy catch.
Marsh started walking off as soon as he made contact, and flipped his bat into the air in frustration.
Mitch Marsh made scores of 13 and 94 against Queensland in Perth. (Richard Wainwright/AAP PHOTOS)
The 32-year-old, who experienced soreness during Australia's recent white-ball tour of the UK, was playing the Shield match as a batter only to protect his body.
WA wicketkeeper Josh Inglis is behind Alex Carey in the Test pecking order, but he enhanced his reputation with scores of 122 and 48 against Queensland.
Bulls bowling allrounder Michael Neser snared 5-68 in the Warriors' first-innings total of 465.
Queensland replied with 367, before WA's declaration shortly after lunch on day four left the Bulls in a fight to survive for a draw.
WA, who are aiming for a fourth consecutive Shield title this season, will face Queensland in a One-Day Cup match at the WACA Ground on Sunday.
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