England once again failed to start a major tournament with victory as Vasili Berezutski's stoppage-time header gave Russia a draw they barely deserved in the Stade Velodrome.
The crucial breakthrough for City came early in the second half as Emre Can was penalised for handling in the box and Mahrez stepped up to fire his side ahead again in the tie.
Fit-again Alexander Isak had opened the scoring in an entertaining first half, sending a composed finish beyond Chelsea goalkeeper Robert Sanchez from 17-year-old Lewis Miley's threaded pass.
Manchester United's Champions League hopes are in tatters after they twice threw away leads before 17-year-old Roony Bardghji's late winner saw Erik ten Hag's side slump to a 4-3 defeat in Copenhagen.
At 17 years, eight months and 11 days, he became France's youngest player since 1914. He marked his debut with a goal to make it 3-0 before going off injured.