The Croatian saved all three break points he faced to defeat Kei Nishikori in the final, 6-1, 7-6 (5), for his second title of 2016 and 16th of his career.
The third-seeded Nishikori dominated the second-set tiebreaker and completed the win in 2 hours, 15 minutes.
Meanwhile, with this 7-5, 6-4 win, Nishikori finally took down a foe he'd failed to take a single set off of in their four previous encounters.
"I saved a lot of important points with my serve", said Nishikori, who had 10 break chances and took one in each set. That gave me some confidence.
After his heroics in the second set, Nishikori was able to steady his game to earn a hard-earned win over Muller, ranked 37.
"In the second I started playing better, I got more aggressive".
"It wasn't an easy match, he had a great serve, a great forehand".
The two-time champion continued his fine recent run, just days after he won the Stockholm Indoor title.
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Nishikori has already qualified for next month's ATP World Tour Finals in London for a third straight edition.
Sunday's (Monday AEDT) contest will be a rematch of the 2014 US Open final, which Cilic won to capture his lone grand slam title.
"I am in the Paris Bercy draw but I am not sure that I will play that event", he said. "We have not played for a long time so I have to see what I have to do tomorrow".
"I'm looking forward to the final", he added. Kei Nishikori dominated Paolo Lorenzi 7-6 (7/3), 6-2 to reach the Swiss Indoors quarterfinals yesterday, with Asia's top player feeling his way back after a series of recent fitness problems.
Cilic now stands provisional ninth for the eight-man field at the Tour Finals after passing Tomas Berdych in the table.
Nishikori came into Saturday's semi-final having not dropped a set all tournament, and it looked for all the world as if he was to continue in that vain against Muller.
Germany's Mischa Zverev defeated U.S. teenager Taylor Fritz 7-6 (7/4), 6-0.