McMillan joined the Munster club as its director of coaching after the Super Rugby Pacific final and has seen it to four games without defeat to date in the competition.
Leinster, a powerhouse of European rugby, had beaten Munster in 21 of their previous 26 derbies.
McMillan told the media after the win, "What it meant to Munster coming up here, it's not about individual performances, it's about the team, the plan the coaches gave us and the hard work we did during the week.
"It's the work as a collective saying you're going to come up with a plan and then actually go out and do it. I'm massively proud to front up with these lads and get over the line tonight."
One of the key contributors to the win was Munster's first five-eighths Jack Crowley, who, based on his performance, has the front running to secure the No.10 jersey for Ireland's forthcoming Test with the All Blacks in Chicago.
McMillan said, "I thought he had a really good game.
"I've been impressed with Jack since he came back from the off-season – he had a real focus about him. He's fit, and he's just calm.
"This week, he started to inject his leadership and his voice a little bit more than what we've seen in previous weeks.
"He was well aware of the occasion, he was up for it and I thought he did a magnificent job."
McMillan wanted to make the contest a dogfight.
"Leinster are too good a side that if you sit and wait and give them a moment to impose their game on you, then you're going to be losing.
"So, we needed to be in the scrap for everything and want to be the hunter, not the hunted. That's the basic gist of it.
"We were under pressure early, particularly our scrum, but we wanted to work hard for each other. We wanted to win all the little moments and we did that."
McMillan praised the performance of captain Tadhg Beirne, the Irish international.
"This guy is the epitome of somebody who's got a high [ceiling] in terms of where he is in his performances. The roof is pretty high, and you don't see too much of a dip in him.
"Our challenge as a team is to raise that floor so that the days between our bad performances and our good ones aren't so big.
"The last couple of weeks have been tough. We haven't been concerned looking at the points, the ladder and patting ourselves on the back. We wanted to be better in our performances, come off the field, look in the mirror and be proud of what we're producing. And today will be one of those days."
