The Russian league runners-up host the second leg on 12 October.
"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.
The club is based in the city of Perm and takes its name from men's team Zvezda Perm, which was dissolved in 1997. Zvezda-2005 won both the Russian league and national cup in 2007, and subsequently reached the final of the 2008-09 UEFA Women's Cup, losing to Duisburg.
Manchester City and England midfielder Jill Scott added to BBC Sport:
Zvezda: Zvarych, Pozdeeva, Pantiukhina, Orlova, Apanashchenko (c), Makarenko, Andrushchak, Nurgalieva, Kipatkova, Korniievets (Korochkina), Akimova.
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"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.
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All results (home and away) list Zvezda's goal tally first.
Event details: NAME: FK Kubanochka Krasnodar - Zvezda 2005 Perm DATE: September 3, 2016 TIME: 14:00 UTC VENUE: Stadion Trud, Krasnodar , Russian Federation
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.
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.
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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.
Manchester City Women: Bardsley, Bronze, Stokes, Beattie, Houghton (c), Asllani, Scott, Duggan, Christiansen (Middag 69), Ross (Parris 84), Walsh.
More details: FK Kubanochka Krasnodar live score, schedule and results Zvezda 2005 Perm live score, schedule and results
"We'll try and dominate (the second leg). We'll go to win the game in Zvezda, for sure."
More details: Zvezda 2005 Perm live score, schedule and results SK Slavia Prague live score, schedule and results
"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.
Event details: NAME: Zvezda 2005 Perm - SK Slavia Prague DATE: November 19, 2015 TIME: 14:00 UTC VENUE: Zvezda Stadium, Perm , Russia
"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.
England midfielder Jill Scott stabbed the new English champions into a first-half lead at the Academy Stadium in their last-32 first leg.
"Credit to the girls for keeping going - it shows the desire in this team."
They also won the Russian league in 2008 and 2009, making it three titles in a row. In 2010 they were third, failing to qualify to the Champions League.
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.
Zvezda 2005 Perm (Russian: "Звезда 2005" Пермь) is a Russian professional women's football club.
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.