Having scored twice against Bradford in the previous round, the 25-year-old Honduras international, embarking on his first full season in English football and being given his chance at Leeds after a productive loan spell at Scunthorpe, took his tally for the season to five with a 20-yard special either side of half-time.
Until the intervention of the former Chivas winger, James Hayter's early goal had looked set to give Doncaster a first home win over Leeds in 60 years but, after Nunez had taken effect, the home side were forced to return their thoughts to a league campaign that has failed to produce a point so far.
Nunez was one of six Leeds changes from the side that drew 2-2 at West Ham on Sunday, with first starts given to Paul Rachubka and Zac Thompson, and their relative unfamiliarity with each other was shown up early on as Doncaster set about finding some form.
They had made three changes themselves but did not have to wait long for the confidence boost they were looking for, taking the lead in the second minute through Hayter.
A hero in Doncaster having scored the winning goal against Leeds in the 2008 play-off final, the striker, making his first appearance since getting injured on the opening day, nipped ahead of Andy O'Brien to touch Giles Barnes' cross beyond Rachubka.
It was the third time Leeds had conceded inside the first 10 minutes already this season and Doncaster were comfortably on top as a result, with Kyle Bennett and former United skipper Richard Naylor going close in the aftermath.
The traffic continued to be all one way, with Rachubka saving well from Bennett and Simon Gillett, before Bennett, one-on-one with the former Blackpool stopper after Hayter's flick had released him, hit the post with a floated effort.
That let-off prompted Leeds manager Simon Grayson to shuffle his pack, putting three men up front and condensing his midfield, and the move had an immediate impact as his side equalised.
Jonny Howson had already seen a strike dip just over the bar by the time the goal came, and when it did it was spectacular. A long ball was headed on by Andy Keogh and Nunez allowed it to bounce once before looping it over Gary Woods from the edge of the area.
Doncaster needed the break to regroup and promptly started the second half as they had the first, albeit without a goal.
It was not for a lack of trying, though, with Bennett twice going close. First he saw his back-post header blocked by Rachubka and then, after a driving run, watched his 20-yard shot flash over.
Their momentum would fade however, and Leeds introduced Max Gradel from the bench in a bid to seize the initiative, with the Ivorian almost delivering instantly as he ran at James O'Connor and shot narrowly over.
Rovers substitute Mark Wilson then tested Rachubka from distance, bringing about his first mistake as he failed to hold the ball and saw it squirm wide of his post
Nunez was not in the mood for extra time, though, and, with seven minutes left, positioned himself on the edge of the box and drilled home a loose ball after Paul Connolly's cross was only half cleared.
Bennett, undeserving of being on the losing side, clipped the post again late on, but his side's resolve had been broken.