The 37-year-old world number three, who first won the Swiss title in 2006, was a break down in each set to Romanian Copil, seeking his first title.
Top-seeded Roger Federer had to work for it, but he ultimately beat Frenchman Gilles Simon on Friday to advance to the semifinals at the Swiss Indoors Basel in Switzerland.
"I'm very happy. I think it was my best performance this week", Federer said. His hour and a half tussle against Marius Copil in the final of the Swiss Indoors aided him to win his 21st ATP 500 crown surpass Rafael Nadal who has 20 of them. "I was a bit unsure of my serve and his return is excellent", said Federer.
Anderson was runner-up to Djokovic at Wimbledon this year but the win in Vienna represented the biggest title of his career.
Wimbledon runner-up and world No 8 Anderson is having a career-best season and won his fourth career title.
However, it wasn't a smooth ride for the 20-time grand slam victor as he dropped his serve five times and was only 59 per cent accurate on his usually sharp first delivery. He kept his foot on the pedal in the second, racing to a comfortable 4-0 lead but had to fight to emerge the victor.
Federer fought back from 5-2 down in the first set to force a tie-break, where he began to take control of the match as he converted seven of eight points to snatch the lead on the hour mark.
The second set produced five breaks of serve - only two to Federer - before Simon struck the victor. But a quick match point opportunity two games later allowed Federer to close as his opponent sent a return over the baseline.