The 21-year-old left-hander top-scored with an unbeaten 179 on a flat MCG pitch on Friday as WA were dismissed for 424 late on day three.
That gave them a 22-run lead, and Victoria were 0-7 at stumps. A lot will need to happen on Saturday for either side to win.
"No doubt it's a flat pitch. There's no secret they're trying to get the Test match to go a bit longer, so we're probably copping that in the Shield," WA captain Aaron Hardie said, referring to last year's disastrous two-day Boxing Day Ashes Test.
"We're certainly hopeful if we get it in the right spot tomorrow ... we'll see what we can do."
Hardie noted that Wasley came to the crease at a tricky time, with WA 3-84 in reply for Victoria's 5-402 declared.
He hit 15 fours and a six in his 337-ball knock that ensured WA would go into the last day on even terms with the home side.
"It's obviously a bit step up from club cricket, but he's done his apprenticeship," Hardie said of Wasley, who made his Shield debut this season.
"To come out and hit the ground running, like he has in the last three games, it's a testament to all the hard work he's put in.
"He's always had a run-scoring ability ... big scores."
Victorian captain Will Sutherland praised his bowlers for sticking to the task. Austin Anzelark, Sutherland, David Moody and Ash Chandrasinghe took two wickets apiece, while Hardie was dismissed for his overnight score of 60.Â
Sutherland was diplomatic about the MCG strip.
"I still think it's a really good wicket. It's obviously slightly more batter-friendly, but it's not a huge difference of bat versus ball," he said.
"I'm not standing here being too negative about the wicket.
"Credit to Wasley, he batted unbelievably. He looks a quality player, and if it wasn't for him we probably would have bowled them out and been able to hopefully set up the game."
There was some chatter on the stump microphones as WA thwarted their opponents.
"I'm definitely not annoyed at the way they went about it. I completely understand ... unfortunately we couldn't bowl them out," Sutherland said.
"I dare say we'll just try and bat as long as we can ... not give them a sniff."
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