Niguez found the net at the end of a slaloming run in the 11th minute in the Spanish capital to set Diego Simeone's side up for the return in Bavaria next Tuesday.
David Alaba sent a thundering shot against the bar for Bayern in the second half, although Fernando Torres hit the post at the other for Atleti.
Manchester City and Real Madrid drew 0-0 at the Etihad Stadium in the other semi-final first leg on Tuesday.