Set a modest target of 155 for victory, Auckland stumbled early losing two wickets before registering a run.
The visiting side slumped further into the mire with Warren McSkimming and Jimmy Neesham reducing Auckland to 55 for five.
But Munro, like he did in the first innings, used his power game to take the attack to Otago.
He was brutal on fellow South African Neil Wagner, whacking him for three fours shortly before the tea break.
Anaru Kitchen also played a significant part, combining with Munro in a crucial 73-run stand for the sixth-wicket.
He was undefeated on 46 and veteran spinner Bruce Martin had the joy of hitting the winning runs in his 100th first-class game.
Otago coach Vaughn Johnson made no excuses for his side's disappointing performance on Sunday.
"We all admitted that [on Sunday] we just didn't turn up," Johnson said.
"We were down on energy, down on intensity and down in execution. We had a very, very poor day. Sometimes, when those things happen, you can catch it up the next day. We nearly did but we didn't. It cost us."
Ian Butler suffered a side strain during the game and will be sidelined for the next few weeks. Craig Cumming took a painful blow to the hand but has not broken any bones and will be available for the game against Central Districts in Queenstown beginning on Friday.
Otago resumed on 77 for four but may as well have been five down with Cumming forced to retire hurt on Sunday night after he was struck on the bottom hand by a rising delivery from Chris Martin.
The night watchman, Nick Beard, did his job, holding out for close to an hour before he was trapped in front by Munro.
Munro was again in the action in his next over, this time trapping Jimmy Neesham in front.
The batsman took his time leaving. He obviously felt the ball would have passed harmlessly over the stumps as replays suggest it may have.
Butler's torrid match continued. He picked up a side strain on Sunday and was forced from the bowling crease. Yesterday he was struck in the neck when he misjudged a delivery from Mitchell McClenaghan.
Derek de Boorder had more luck. He posted 50 in the first innings and once again held the middle order together with defence first and then attack second. With wickets tumbling, de Boorder was left with little choice but to play a few shots and was dismissed trying to manufacture a pull shot on 57.
Cumming came out at No 11 with his badly bruised hand and advanced his score from 11 to 19 before McSkimming was the last man out when he clipped the ball to Jeet Raval at short leg.
Auckland had a double setback before getting the scoreboard moving. Raval capped a disappointing game when he repeated the mistake he made in the first innings, nicking out to Wagner.
Tim McIntosh needed just 51 runs to overtake Trevor Franklin as Auckland's leading run-scorer in first-class cricket but completed a pair for the match when he was run out.
Further calamity awaited.
McSkimming found a great line and length and with some help from the pitch jagged two deliveries back which accounted for Brad Cachopa and Neal Parlane. Cachopa, at least, offered a shot but his defence was not up to what was a superb ball.
Parlane just plodded a foot down the wicket and shouldered arms and was bowled.
When Gareth Hopkins was undone by a similar delivery, this time by Neesham, Otago would have felt it was one wicket away from getting at Auckland's tail.
Munro joined Kitchen and by tea the pair had added 51 to put their side on course for victory.
There was final day drama in the two other Plunket Shield matches yesterday as Northern Districts and Wellington eked out fourth-day victories, APNZ reported.
The Knights staged a late fightback to beat Central Districts by 65 runs and the Firebirds chased down 280 to beat Canterbury by five wickets.
No result was secure going into the final day but, after some ups-and-downs, the three winners broke clear on top of the Plunket Shield standings at the halfway mark of the competition.
Northern Districts lead on 64 points, with Auckland in second place on 50 and Wellington right behind on 45.
