After two days of the opening Shield matches, Renshaw was the major winner in round one of the bat-off for top-order spots.
Incumbent Test opener Usman Khawaja and Queensland Marcus Labuschagne also scored half-centuries, with the home side well-placed on Sunday at Allan Border Field.
They were 1-248 after Tasmania was dismissed earlier in the day for 379.
Renshaw was 114 not out, making the most of several chances, and Labuschagne had made 54, while Khawaja was dismissed for 69.
Fellow openers Sam Konstas and Cameron Bancroft fell cheaply in Perth's bowler-friendly conditions, while No.3 Marcus Harris was run out for 61 when looking set at Adelaide Oval.
On Saturday, Tasmanian opener Jake Weatherald made 67.
The most recent of Renshaw's 14 Tests was against India in February, two years ago.
He started the domestic season on the periphery of discussions as Australian selectors try to sort out their top order for the first Ashes Test from November 21 in Perth.
But Sunday's unbeaten knock, from 214 balls and featuring 14 fours and a six, was excellent timing.
Renshaw said he had tried to shut out the speculation ahead of the Ashes and play well for his state.
"It's hard - you have to get rid of a lot of things, external noise, off your phone and stuff but I just want to try and go out there (and play)," he said.
"I know that when I'm doing my job for Queensland, opening the batting well, we're generally winning games.
"I had a good opportunity to get in this afternoon. It felt like it was going to be a good batting wicket for us.
"There were some tough periods, but a really good position for the team now.
"There's a lot of noise that people can and can't deliver, but I just want to go out there and have fun and play like it. If you told 12-year-old Matt that he was going to score a Sheffield Shield hundred, he'd be pretty pumped."
Tasmania resumed on 6-299 and Jake Doran made 66, while Queensland paceman Michael Neser took 4-75.
Renshaw added they would aim to keep batting for as long as possible on Monday and build a solid first-innings lead, adding there were cracks appearing in the wicket.
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