Zurich's Sangone Sarr scored the only goal four minutes before halftime after Lugano keeper Mirko Salvi failed to collect the ball from a corner.
Lugano missed a penalty nine minutes earlier when Mattia Bottani's effort was saved by goalkeeper Anthony Favre.
The win means Zurich have qualified for next seson's Europa League where they will start in the group stage.
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However the team, Swiss champions 12 times and one of the country's most popular clubs, will be in the second tier next term after being relegated on Wednesday as the bottom team in the Swiss Super League to end a 28-year run in the top flight.
They were one point behind Lugano after both sides won their final matches.
The match was a chance for Lugano coach Zdenek Zeman to win the first major competition of his career at the age of 69.
The Czech-born manager, an outspoken advocate of attacking football, has coached more than a dozen clubs in neighoubring Italy, including Lazio, AS Roma and Napoli, but his only titles had been in the second and third divisions.
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