Voges made a career-high 235 in WA's score of 5-447 declared, which left Queensland needing an unlikely 301 for victory off just 41 overs.
With limited time remaining, the Bulls were happy to play out time, reaching 2-76 off 30 overs before both sides agreed to halt proceedings at 5.15pm local time in Perth.
Although Queensland managed to secure first-innings honours on a batter-friendly WACA wicket, they remain bottom of the Shield table with just four points to their name.
WA (eight points) sits in fourth spot, but they have some work to do if they are to overhaul the second-placed Redbacks (16) or ladder-leading NSW (18).
Warriors spinner Ashton Agar finished with figures of 2-22 from 11 overs, which included a spectacular catch off his own bowling to remove Luke Pomersbach for 40.
But the day belonged to Voges
Voges cracked 31 boundaries in his 457-minute stay at the crease, with his knock lifting WA back into the contest after they were left with a 147-run first-innings deficit.
Queensland had their heart set on snaring an outright win when the Warriors resumed at 3-182 on the final day.
Bulls skipper James Hopes boosted his side's hopes by snaring the key scalps of Shaun Marsh (47) and Mitch Marsh (27) before lunch.
But Sam Whiteman (74no) and Voges combined for an unbeaten 162-run stand to snuff out Queensland's chances.
Hopes was Queensland's best bowler with figures of 3-73 from 30.3 overs.
But he didn't seem all too happy at how long it took for WA to declare.
With WA's lead on 299, Hopes ordered all of his fielders near the boundary in a bid to stem the runs, and also send Voges a clear message that it was time to declare.
One ball later - at 2.48pm - WA declared.
Queensland opener Luke Pomersbach was named man-of-the-match for his knocks of 159 and 40.
Bulls coach Stuart Law was disappointed his side weren't given a legitimate crack to secure victory.
"Seven an over - it's a back-handed compliment in a way," Law said.
"A lot of teams do fear us, which is a good thing. But it's the second time it's happened to us - a ridiculous run chase on the last day."
WA skipper Voges said the fact the pitch held together so well prompted him to declare later than he initially planned.
"For being behind the game for so much of the game, we just felt that we didn't want to hand Queensland anything too easy," Voges said.
"Three hundred off 40 overs is pretty conservative, but that was our thinking."