Federer, bidding to add to his substantial collection of honours by steering the Alpine nation to a first Davis Cup triumph, delighted a capacity crowd in the Palexpo Arena with a 7-6(5) 6-4 6-4 victory.
"Margins were small in the first set," Federer said. "In the second set I was finally able to get the break and that broke the deadlock for me a little bit. I was able to play with the lead which is always easier.
"It was quite frustrating at times when the court is pretty quick. We didn't think it was going to be this fast but when you do serve well you really do feel the benefit."
Seventy-sixth ranked Bolelli, who was surprisingly selected for singles duty ahead of Andreas Seppi by virtue of having fewer previous defeats against the 17-times grand slam champion, stuck to his task impressively on the blue indoor court.
He saved two set points in the opening tiebreak but fired a backhand wide on Federer's third, to the relief of his 33-year-old opponent who was far from his fluent best.
World number three Federer finally secured the first service break of the match in the seventh game of the second set and cruised on to the 36th singles victory of his Davis Cup career.
DOMINANT WAWRINKA
Australian Open champion Wawrinka made light work of world number 17 Fognini and despatched the Italian 6-2 6-3 6-2 in one hour 30 minutes. After struggling to rediscover the early-season form that won him the Australian Open title, Wawrinka has spoken of his desire to win the Davis Cup and he showed his intent by firing 16 aces and 37 winners past Fognini.
The fiery Swiss snatched an early break in the opening set before racing into a 4-1 lead as Fognini had no answer to the world number four's clean hitting.
More crisp and punchy strokes followed over the next two sets as Wawrinka ensured Switzerland took a 2-0 lead into Saturday's doubles. Switzerland have reached the final once, losing to the U.S. in 1992, while Italy got there in 1998, going down to Sweden.
(Reporting by Martyn Herman and Michael Hann; editing by Ken Ferris and Toby Davis)
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