Batting for the Prime Minister's XI, the 27-year-old outperformed other contenders for the soon-to-be vacant Test opener's job with an unbeaten 136.
His side reached 4-367 in their first innings at stumps on days three at Manuka Oval, still 34 runs behind the tourists with the final day's play almost certain to bring a draw.
But Renshaw has sealed honours in the so-called "bat-off" in this match among the leading Warner replacements, with openers Cameron Bancroft (53) and Marcus Harris (49) and allrounder Cameron Green (46) not making the most of their starts.
He denied there was extra motivation for his classy knock, instead crediting his much-improved mindsight.
"It's just another game of cricket, all the other stuff takes care of itself," Renshaw told reporters.
"Only a couple of years ago, I took a break from the game because of how much I was taking it seriously, that was a really big learning curve for me just to go 'why am I playing this game'?
"It's not to play for Australia, obviously I want to and that's the goal but at the end of the day, I'm going to try and enjoy myself."
The 14-Test left hander adds Friday's century to 348 Sheffield Shield runs this season at an average of 32, and Warner has previously endorsed him as the leading contender for his job.
Outside of a 10-minute period where he hoisted Pakistan spinner Abrar Ahmed for two fours and a huge six, Renshaw played a particularly defensive innings at No.3 that featured 335 balls.
"It was taking a lot out of me to keep grinding down," he said.
"There were some times where I felt like I couldn't get the ball off the square.
"My game has been transitioning really well this season (from) a couple of little conversations with batting coaches and myself just to work out what I'm trying to do."
Green played some nice shots early, but reached at a wide Faheem Ashraft delivery and was caught behind just as a big score beckoned.
Bancroft arguably entered the "bat-off" in pole position as the Shield's top run-scorer this season, while Harris has regularly travelled with the Australian side as the spare batsmen.
Punters at Manuka Oval perhaps were given a preview of a future Australian leader, with 24-year-old Nathan McSweeney playing some exquisite square drives on the way to his 40.
A brilliant diving catch from Mir Hamza denied him the chance for a statement score.
McSweeney, who is captaining the PM's XI, has been earmarked as a future national team leader after skippering Australia A earlier this year.
Pakistan had rested first-choice pace bowlers Shaheen Shah Afridi, Hasan Ali and Mohammad Wasim, and spinner Ahmed exited the tour match on Friday nursing what appeared to be an injured calf muscle.
If they want a specialist spinner in Perth, they may need to pick 37-year-old Noman Ali who also sat out the tour match.
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