The Auckland all-rounders flogged 157 runs from 120 balls to help their side reach 518 for eight declared.
Munro finished unbeaten on 112 from 79 deliveries, with de Grandhomme setting a more sedate pace of 65 from 61.
At stumps on day three, Otago was 23 without loss in its second innings and trailing by 263 runs.
The Volts will have to work hard just to avoid defeat when the match concludes today.
With Canterbury enjoying a healthy lead at the top of the competition table, Otago needed to secure an outright win to have any realistic chance of winning the tournament.
Earlier in the day, though, it was all about patience. And when it comes to patience, Auckland left-hander Tim McIntosh has it in abundance.
The former test opener combined with Jeet Raval in an enormous 246-run partnership for the third wicket, which put Otago on the back foot.
McIntosh brought up his 19th first-class hundred off 314 balls in 426 minutes, or, put another way, his 100th run took 52.2 overs and seven hours six minutes. Blimey.
He eventually got out in the most unusual way - hit wicket. On 116, and having displayed admirable concentration, he stepped back on to his stumps. Someone cruelly suggested he had fallen asleep and fell on them. Actually, he just step back a wee bit too far and his right foot brushed leg stump.
It was terribly unfair comment - funny, though - but McIntosh's dismissal did inject some spark into the game.
Munro and de Grandhomme batted with furious intent. Given 63 overs were lost on day two, Auckland's initial lack of progress seemed an extravagant waste of an opportunity to advance the match.
Raval, who was fortunate to survive several opportunities early in his innings of 143, played nicely yesterday. He resumed on 46 and really does drive the ball well. He is quick to get into position to pull the ball if the bowler drops short, and has a solid defence.
The second part of his innings was without incident and he has probably put his name in the minds of the selectors. The one area the Black Caps are struggling in at the moment is at the top of the order. Canterbury's Tom Latham is the first in line but big hundreds like Raval's innings help.
He got out in disappointing fashion, though, hitting a simple catch to Nathan McCullum at mid-on.
Technically, Munro was dropped on 34 by Mark Craig, but it really was only half a chance. It was full-blooded drive that Craig had the misfortune of trying to stop.
