Manchester City began their first Women's Champions League campaign with a 2-0 home win over Zvezda 2005.
England midfielder Jill Scott stabbed the new English champions into a first-half lead at the Academy Stadium in their last-32 first leg.
Scott then clipped the inside of the post after half-time, before Lucy Bronze added a late second with a strike from the edge of the area.
The Russian league runners-up host the second leg on 12 October.
City controlled the first half and, after Scott's opener, could have been further ahead at the break but Toni Duggan was denied by a fine, reaction save and Steph Houghton's header struck the crossbar.
Zvezda - who reached the last-16 stage in both of the past two seasons - were restricted to shots from range and rarely looked likely to score an away goal.
Thursday's game came four days after City won the Continental Cup final to complete a domestic double but, although showing some hints of tiredness, they created numerous chances and could have had a penalty when Kosovare Asllani was brought down in the Zvezda area.
Nineteen-year-old midfielder Keira Walsh was exemplary in midfield, but her half-volley from range bounced narrowly wide, before Bronze scored in stoppage time to give City what could prove to be the tie's decisive goal.
Manchester City manager Nick Cushing told BBC Sport:
"We weren't at our best tonight, but we were good. I knew Zvezda would be resolute tonight and try and limit us. They're a tough team. They were very organised.
"We dominated the game. We were in control at 1-0. 2-0 is better, but I was content at 1-0. We wanted to win and keep a clean sheet, so the objective was met for us.
"We'll try and dominate (the second leg). We'll go to win the game in Zvezda, for sure."
Manchester City and England midfielder Jill Scott added to BBC Sport:
"It was important that we got the win today. If you'd said at the start of the game, 2-0, we'd probably have taken it.
"It has been a busy period for this team and we should be very proud of what we've achieved in the past few weeks.
"Credit to the girls for keeping going - it shows the desire in this team."
Manchester City Women: Bardsley, Bronze, Stokes, Beattie, Houghton (c), Asllani, Scott, Duggan, Christiansen (Middag 69), Ross (Parris 84), Walsh.
Subs not used: Hourihan, Corboz.
Zvezda: Zvarych, Pozdeeva, Pantiukhina, Orlova, Apanashchenko (c), Makarenko, Andrushchak, Nurgalieva, Kipatkova, Korniievets (Korochkina), Akimova.
Subs not used: Raspopova, Sinko, Galay, Koshneva, Kasatkina.
Referee: Monika Mularczyk (POL)