Renshaw's innings of 112 was the cornerstone of Somerset's 216, with paceman Jack Brooks taking five for 57 for the visitors on the second day of the First Division clash at Taunton.
But on a day when 20 wickets fell, Yorkshire were bundled out for 96 in reply as Lewis Gregory and Tim Groenewald took three wickets apiece before Somerset closed on six without loss in their second innings -- a lead of 126.
Renshaw only joined Somerset as their overseas player after the southwest county tore up compatriot Cameron Bancroft's contract as a result of his involvement in the ball-tampering scandal that overshadowed Australia's recent tour of South Africa.
Renshaw repaid Somerset for the late call-up with 101 not out on debut in a win over Worcestershire last week.
And having made a fifty on Saturday that was entirely composed of boundaries the 22-year-old, born in Middlesbrough, northeast England, went on to an 86-ball hundred including 14 fours and four sixes to achieve the impressive distinction of a hundred before lunch following Friday's opening-day washout.
"It was a pretty different innings to my normal game but having assessed the wicket this morning, I didn't feel comfortable just fending at it," Renshaw told Somerset's website.
"I was better if I was playing full cricket shots," he added after a hooked six off Brooks saw him to three figures.
"They were bowling really well and I felt that if I fended one and nicked off, it would really annoy me."
Renshaw, who has made 11 Test appearances, added: "I tried to take the game on and put pressure on their bowlers and tried to come out on top. I guess it was just my lucky day."
Australia have not won the Ashes away from home since 2001, with their recent Tests in Britain often seeing their top-order struggle in the swing-friendly conditions that are a hallmark of English first-class cricket.
But at this rate of progress, Renshaw should be well-prepared for next year's Ashes tour, just as Australia great Greg Chappell, one of cricket's outstanding batsmen of all time, benefitted from playing for Somerset before the 1971 series in England.
"The wicket is quite interesting," said Renshaw. "The odd ball starts swinging and it's nipping about a little bit, which is quite different to what I am used to.
"It will be a good challenge for me to try and bat a bit tomorrow (Sunday) and try to put more pressure on their bowlers."
He added: "This has been a good start for me but there is a lot of cricket to go this season. Hopefully, I can carry on like this."
First Published: April 29, 2018, 8:23 AM IST