Mehta opened the Monday evening concert at the Walt Disney Concert Hall with stirring renditions of the American and Israeli national anthems, followed by a program of Beethoven, Schoenberg and Berlioz.
Finally, giving in to prolonged standing ovations, Mehta and the orchestra added an encore.
Outside Disney Hall, Women in Black rallied some 50 supporters of both genders for a protest.
The vigil was silent, but demonstrators conveyed their sentiments through large signs with such messages as "End Israel Apartheid in Palestine" and "Boycott Israel Philharmonic."
Last October, Women in Black sent a letter to the Israel Philharmonic, asking its members to publicly oppose "Israeli apartheid."
Receiving no response, the group followed up with a letter to Los Angeles Philharmonic president Deborah Borda and music director Esa-Pekka Salonen demanding cancellation of the two concerts.
Borda rejected the demand, writing that "We will never support the silencing of artists from any culture as a means of political action."
Security was noticeably tight, with random body checks at the entrance and the closing of the 2,000-car garage underneath Disney Hall.
Inside the hall, Mehta and the orchestra performed Beethoven's Leonore Overture No. 3 with great strength, Schoenberg's Verklärte Nacht with great subtlety and Berlioz's Symphonie Fantastique with great -- but wholly appropriate -- bombast.
During the Schoenberg, only the renowned string section performed. During the Berlioz, the orchestra expanded to include a full brass section, two harps and at least five percussionists, among them, one man sporting a full beard, payes and a yalmulke. Schoenberg's grandson E. Randall Schoenberg, the lawyer who recovered Nazi looted artworks by Gustav Klimt from the Austrian government, listened from the front row.
After repeated standing ovations, Mehta raised his baton and led the orchestra through the Donner und Blitzen Polka by Johann Straus the Younger -- a rousing end to a thrilling evening.
The orchestra's American tour, which included performances in New York's Carnegie Hall and San Francisco's Davies Symphony Hall, were part of the Israeli Philharmonic's 70th anniversary celebration.