NBC triumphed Monday over its network rivals and Cable News Network in becoming the first to get Soviet approval for an interview with Soviet leader Mikhail S. Gorbachev before his summit conference in Washington with President Reagan. Anchor Tom Brokaw will conduct the interview with Gorbachev in Moscow this Sunday for a one-hour taped program, "A Conversation With Mikhail S. Gorbachev," to air Monday ( at 8 p.m. (PST). There are no restrictions on questions Brokaw can ask, said an NBC News spokesman. The spokesman added that consultant Gordon Manning, who has tried to arrange a Gorbachev interview for two years, helped land this one. Manning once was an executive at CBS News, which also sought a pre-summit interview with Gorbachev but was turned down by the Soviets. CBS News President Howard Stringer has asked Gorbachev to reconsider the unexplained rejection, but the Soviets have yet to reply. ABC is still waiting for a reply to its request, but CNN says its request was rejected Monday without explanation.