The eighth seed and winner in 1996 needed just a little over two hours to dispose of the 26th-ranked Lapentti, collecting his second title of the season. Costa's victory also marked the eighth time in nine years that a Spaniard has walked away with the Swiss crown.
Even the sight of a non-Spaniard in the Swiss final has been rare. Lapentti joins the German Boris Becker as the only non-Spaniard to play for the title since 1995.
Searching for his first title in four years, Lapentti began looking determined, breaking Costa's opening serve to jump to a 3-0 lead. But Costa refused to panic, breaking back at 4-3, and then won the tie-break 7-4.
"The key was the first set," said Costa, who will move back into the top 25 of the world rankings today. "If he had won it I think the match would have changed a lot.
"At the beginning of the second set I had the feeling I was going to win. I think he was down a little after the first set."
With the opening set taking 58min and the capacity crowd settling in for a long afternoon, Costa picked up the pace. Working from the baseline, he found his rhythm and range in the thin air of the Swiss resort, speeding through the second set, and continued to apply pressure in the third, breaking Lapentti's first two serves.
Lapentti's performance here, which included wins over two other Spaniards and the former Swiss champions, 1997 winner Felix Mantilla and defending champion Alex Corretja, will be enough to join Andres Gomez as the only two Ecuadorean players ever to reach the top 20 rankings.
Chris Wilkinson failed to pick up his third Tour title yesterday after he lost the final of the Bristol Challenger Trophy to Raemo Sluiter, of the Netherlands, 6-3, 6-7, 7-6.Reuse content