Fuster hit a right-footed shot low past home keeper Aleksandr Goryainov to give his side the advantage heading back to Greece next week, and to make matters worse for the home side they had Edmar sent off eight minutes from time.
Metalist may have started as narrow favourites but the visitors swept into the game on the back of eight straight wins in all competitions and were clearly brimming with confidence.
Papa Gueye and Jose Sosa looked dangerous out wide for the hosts early on, but it was the visitors who had the first real chance when Goryainov was forced to punch away a Kevin Mirallas corner.
Cleiton Xavier had a long-range effort blocked for Kharkiv in the ninth minute, then Giannis Maniatis tried much the same at the other end but had his effort blocked by the busy Gueye.
With long-range efforts the order of the day, Olympiacos keeper Balazs Megyeri saved from Sebastian Blanco, then Jonathan Cristaldo also fired well wide from 20 yards for the home side.
The home side continued to create the majority of chances, with two from Vinicius Fininho saved by Megyeri, as was a Cleiton Xavier free-kick. Maniatis shot over the bar from 25 yards for Olympiacos.
Fuster drove home the opener from six yards shortly after the break but the lead was almost short-lived as the hosts should have been level within four minutes, Edmar heading a Sosa cross over from point-blank range.
Edmar had another shot blocked and Freda Taison also headed over as the Ukrainians piled on the pressure. The increasingly busy Megyeri saved again from Taison while Marko Devic shot wide.
Cleiton Xavier shot over again in the 78th minute but the expected Metalist push in the final stages never really materialised, with the visitors holding onto their slender lead with relative comfort.
The hosts' hopes were further hit 10 minutes from time when Edmar was sent off for serious foul play following a foul on Maniatis.