Pep Guardiola‘s men made a fast start in Germany and took the lead just before the half-hour mark.
Mahrez finished expertly after good work in the build-up by Jack Grealish and Ilkay Gundogan, claiming his 75th goal for City.
The hosts emerged with more attacking intent after the interval, first forcing Ederson into a smart save from Timo Werner’s powerful cross towards the onrushing Emil Forsberg.
The Brazilian then made two sharp stops shortly after, from Andre Silva and Dominik Szoboszlai, but could not do anything to prevent Josko Gvardiol’s equaliser as the defender rose highest to head into the net with 20 minutes remaining.
Gundogan almost provided the perfect response, firing towards the bottom corner, but Janis Blaswich got down smartly to parry the ball away.
CITY+ | SIGN UP TO ACCESS EXCLUSIVE CONTENT
Neither side could find the winner late on, meaning the tie is finely poised ahead of next month’s return leg at the Etihad Stadium.
View the best images from the Red Bull Arena via our gallery below.