Both Premier League clubs Arsenal and Chelsea were initially drawn to be at home in the first leg.
Manchester City now trail Liverpool by 10 points.
Arsene Wenger's side ended a run of three successive Premier League defeats with a solid display at the Emirates Stadium.
World Champions Germany, who face Northern Ireland on Tuesday in Group C, needed Shkodran Mustafi to break the deadlock against Ukraine before midfielder Bastian Schweinsteiger sealed the 2-0 win on a break in injury time.
Defender Shkodran Mustafi powered home the opener from Toni Kroos's free-kick after just 19 minutes of Sunday's Euro 2016 encounter and Bastian Schweinsteiger wrapped up the win for Germany in added time, moments after coming off the bench against Ukraine