The opener cruised to 125 before the hosts declared at 3-289 and left the Blues a target of 418 for an unlikely victory in Brisbane.
NSW were 1-11 at stumps on Monday, Nic Maddison out without scoring after shouldering arms to a straight Michael Neser delivery.
Sam Konstas was unbeaten on nine, while nightwatchman Ross Pawson survived 26 balls for one run in the shadows of stumps.
Earlier Renshaw and Jack Clayton (76) consolidated the Bulls' advantage after Blues captain Jack Edwards (108) had done his best to keep NSW in the conversation.
Clayton, fresh off 134 in the first innings, seemed destined for twin hundreds in the match before he pulled up with a hamstring complaint and retired hurt.
Renshaw pushed on, accelerating into triple figures and finding a friend in Jimmy Peirson (44 not out off 40 deliveries).
Former Test opener Renshaw began the Shield season slowly and was overlooked for a berth against India.
But he found form later in the year and now has two red-ball centuries either side of some dominant one-day and Big Bash League innings.
"I had a really good bit of momentum in the last two, three Shield games after that first hundred," Renshaw said.
"I wanted to keep that momentum going ... and today kept it nice and simple.Â
"I back our bowlers to do the job (and bowl out NSW on Tuesday). It might be at 5pm, might be at 3pm."
The Blues made 259 thanks to Edwards, but still conceded a 128-run lead after winning the toss and opting to bowl first.
Sent home ahead of Australia's second Test in Sri Lanka, Konstas will have his chance under pressure in what is his first match at the venue.
The Bulls have just one win and three draws from six matches this season, but could jump fourth-placed NSW with a victory and remain in the hunt for a top-two finish with three games remaining.
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