De Minaur earlier returned to the title clash when Briton Jack Draper retired from their semi-final meeting because of an undisclosed issue while trailing 6-3 2-6 4-0.
It will be Ruud's second final in the country in as many weeks, but he will hope for a better result on Saturday after losing in Los Cabos to another Australian, Jordan Thompson.
The Norwegian was pushed to the limit by world number seven Rune in physically demanding conditions in Acapulco.
"I'm like a cockroach, not going anywhere, just creeping back in," Ruud joked when asked about his ability to respond after seemingly getting knocked down.
Rune came out firing and took the opening set. He was a point away from a break in the third game of the next set after finishing a long rally with a forehand winner at the net, but the Dane suddenly began to lose momentum.
The 20-year-old eventually squandered the opportunity as sixth-seed Ruud regrouped and levelled at one set all, switching to a more aggressive style of play.
"It was a tough start, Holger came out firing bullets from the forehand and backhand. I didn't have too much time to play my game and was frustrated at times," Ruud said. "Luckily with a break in the second, it turned around a bit."
Ruud, who had beaten the Scandinavian five of six times on clay, sensed the opportunity to extend his advantage over Rune, who appeared hampered by illness and needed medication before the start of the third set.
But Rune drew huge cheers from the crowd by breaking for a 3-1 lead with an unbelievable forehand return from deep after Ruud thought he had won the point with an overhead smash.
Ruud clawed his way back and went up 5-4 as a cramping Rune wobbled with a couple of double faults, before the world number 11 settled the contest on serve.
"In the third set it got a little physical, and Holger seemed like he was struggling... He broke me, which is frustrating, but you try to get balls back in and make him run and fight for points," Ruud said.
"Luckily I was able to do that. Some unforced errors crept up on him, and I served well in the last game to close it out."
