New Zealand A 224 (McConchie 74, Johnson 4-53, Agar 4-56) and 31 for 0 need 334 more runs to beat Australia A 370 for 6 and 218 for 2 dec (Renshaw 78, McSweeney 69*, Ward 67*)
Renshaw followed up his first-innings knock of 112 with a quick-fire 78 off 72 balls as the visitors declared at 218 for 2. It set New Zealand A a victory target of 365, and they went to stumps on day three at 31 for 0, needing a further 334 runs to win.
Renshaw's big knocks come at a perfect time for him given the question marks surrounding David Warner's Test future.
Warner's lean run with the bat in the Test arena over the past 12 months means he's no certainty to be picked for the World Test Championship final against India at The Oval in June and the ensuing Ashes series in England.
Renshaw played the last of his 14 Tests in India earlier this year, posting scores of 0, 2 and 2 in his only three knocks of the series before being dropped.
Despite those failures, the 27-year-old remains in the Ashes mix, and his form at Bert Sutcliffe Oval will further strengthen his chances.
Renshaw cracked 11 fours and two sixes in the second innings as Australia A ramped up the run-rate in a bid to give themselves enough time to bowl out the hosts for a second time.
Mitchell Swepson, who is aiming to snare a ticket to the Ashes as Australia's back-up spinner, finished with 1 for 51 from 12 overs.