The Bushrangers made 450 in their first-innings in reply to the Warriors' 243 to lead by 207.
With WA progressing to 3-281 at tea on day four, Victoria skipper Aaron Finch and Mitch Marsh agreed no outright result would be reached, ending the match.
Openers Jonathan Wells (107) and Will Bosisto (98) endured a tricky session after tea on day three but batted the visitors to safety with a 195-run partnership.
Bosisto top-scored with 57 and wicketkeeper Josh Inglis made a handy 46 in the first innings after the Warriors won the toss and elected to bat, while Victorian spinners Fawad Ahmed and Jon Holland took three wickets each.
Glenn Maxwell pressed his claims for a Test recall with a commanding 96 on day two, while wicketkeeper Seb Gotch (98) fell agonisingly short of his maiden first-class century.
WA spinner Ashton Agar finished with figures of 4-119 from 50 overs in his first-class return after suffering a broken finger on Australia's tour of India.
"It was one of the flattest wickets I've ever played on," Mitch Marsh said.
"It was disappointing that we couldn't get a result, but I thought we fought hard.
"It was always going to be very hard to take 20 wickets on that wicket ... it was a long four days."
The result means Victoria remain bottom of the Shield table after five rounds without a win, while the Warriors are fourth.
The Shield season will resume in February after the Big Bash League break.