Ukraine jumped from the fourth place to the top of Group I on 14 points, one above Croatia and Iceland, who lost to Finland.
Ukraine travel to Iceland on Wednesday morning AEST and Croatia still have one game in hand after their game against Kosovo was abandoned due to heavy rain.
Yarmolenko scored the opener for Ukraine in the 18th minute as he fired low into the left corner to finish off a good move. Yarmolenko, who moved from Dynamo Kiev to Borussia Dortmund this week, calmly struck the second goal into an unguarded net three minutes before half-time.
Iceland's hopes were hit by a 1-0 loss in Finland.
Alexander Ring's eight-minute free-kick ended up being the deciding goal, while Iceland finished the match with 10 men after the 75th-minute dismissal of Rurik Gislason, who picked up two yellow cards in three minutes.
Turkey are two points further back in fourth.
Albania enjoyed a 2-0 home win over Lichtenstein in Group G courtesy of second-half goals from Odise Roshi and Ansi Agolli.
Lower down the group Israel slumped to a shock 1-0 home defeat to FYR Macedonia, Goran Pandev with the 73rd-minute winner.
Serbia moved two points clear of the Republic of Ireland at the top of Group D thanks to a routine 3-0 home victory over bottom side Moldova.
Mijat Gacinovic opened the scoring in the 21st minute, with Aleksandar Kolarov making it two eight minutes later.
Newcastle United's Aleksandar Mitrovic wrapped up the win 10 minutes from time as Serbia took full advantage of the Republic of Ireland dropping points in Georgia.
