With a combined age of 72, it was the oldest singles final on the ATP World Tour since Hong Kong in 1976 when 42-year-old Ken Rosewall defeated 30-year-old Ilie Nastase.
Earlier, Estonia's Anett Kontaveit, one of the rising talents of the WTA tour, won her first tour title in the women's final, beating Russian Natalia Vikhlyantseva 6-2 6-3.
Muller, Luxembourg's best-ever player, has enjoyed a remarkable season, winning his second title of the year here after previously never having managed to earn one in 13 years of trying.
The left-hander even blasted 22 aces to outperform Karlovic, the most prolific purveyor of aces the game has ever seen, winning two tiebreaks after neither man had enjoyed even the sniff of a break point in the one hour 35 minute contest.
The 21-year-old Kontaveit, who had already reached one WTA final and beaten world number one Angelique Kerber this season, overcame a dip in concentration at the start of the second set to earn her victory in just under an hour and a quarter.
The 20-year-old Vikhlyantseva, another promising talent, was outplayed in the opening set but after breaking to take a 3-1 lead in the second, Kontaveit moved into overdrive to halt the comeback swiftly and win the next five games.
The victory will shoot the young prospect from Tallinn from world number 49 to a new career-high of 36 when the rankings are announced on Monday.
(Reporting by Ian Chadband; Editing by Toby Davis)
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