Frei, who is quitting international football at the end of the season, was given a standing ovation when he was substituted in the second half, a stark contrast to the jeers he received in two home games earlier this season.
Olexandr Alijev and Yvgeni Konoplianka replied as Ukraine twice came from behind at a half-empty Stade de Geneve.
Switzerland went ahead five minutes before the break when Frei floated a free kick into the top corner - his first goal for Switzerland since the World Cup qualifier in Latvia in September last year.
Ukraine levelled quickly after the break with a Olexandr Alijev free kick which was deflected into the goal off the back of his team-mate Andriy Yarmolenko.
The hosts went ahead again just after the hour mark when Frei slid in unmarked at the far post to turn in Hakan Yakin's free-kick for his 42nd goal in 82 appearances.
However, Ukraine's Konoplianka had the last laugh, scoring with a vicious dipping shot from the edge of the area.
Frei, 31, was jeered after missing a penalty against Australia in August and also in the 4-1 Euro 2012 qualifier win against Wales last month. He said he had wanted to quit immediately but was dissuaded after receiving letters of support from fans.
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