The 22-year-old top seed and world number one beat Andreev 6-2, 6-3, 5-7, 6-3 on clay to claim his first title on Swiss soil at the fourth attempt on Sunday.
"At last, I have won a final in Switzerland," said a relieved Federer. "It has not been easy, but it feels great to do it now. I am so happy to win here. I was not favourite for my first two finals, indoors in Basel when I lost and last year Jiri Novak played really well here. This time it is my turn at last."
It was Federer's 51st victory of the season, his seventh title in seven finals this year and brought him the 18th title of his career. It also extended his current sequence to 25 wins in 26 matches, a satisfying statistic and some vengeance after losing last year's title in five sets to Czech Novak.
But Federer needed the support of the crowd of more than 5,000 enthusiastic home fans to help him through a tough contest in his first meeting with Andreev on a day of intermittent sunshine and cold winds.
SUBLIME
He cruised through the opening two sets in 48 minutes, with two breaks in the first and one in the second, but then, as tiredness crept into his game, seemed to lose his energy and rhythm in the third. Loose shots were mixed with sublime angled passes.
After going ahead with a break in the third game, fatigue set in and the Russian, who was playing in his first ATP final and turns 21 on Wednesday, broke back twice to gain confidence, force a fourth set and set up a nightmare scenario for the tired Federer.
But in the fourth set, Federer once again dug deep into his reserves and, after saving a break point against him in the fourth game, he broke Andreev in the fifth with a clinical running forehand pass that left the Russian stranded on the baseline.
After holding serve, Federer broke him again to clinch the match in the ninth when the Russian netted with a forehand as he attempted to save the second of three match points conceded by a series of poor serves.
"He is a great player," said Andreev. "Anyone who can win Wimbledon on grass one week and then come and win a tournament like this on clay a week later has to be the number one in the world. It is two completely different kinds of tennis."
Federer has now gone a complete year since he last lost a match in the final of a tournament, to Novak, in Gstaad, in July, 2003.
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