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Zdravko Kuzmanovic had the first opening for Inter midway through the half, but he could only drag his effort wide of the target.
Kuzmanovic came even closer for the visitors minutes before the break when he saw his looping header drop just over the bar.
Fredy Guarin almost gave Inter the lead five minutes after half time, but after latching on to a ball over the top, he could only direct a header over the bar.
On the hour-mark Konoplyanka came within inches of giving his side the lead, but his curling effort went narrowly wide of the far post.
The hosts were dealt a blow in the 68th minute when Ruslan Rotan was sent off for picking up a second yellow card.
Inter soon made them pay and took the lead three minutes later when D'Ambrosio latched on to Guarin's header, before squeezing a shot through the legs of the keeper.
The visitors dominated from then on and comfortably saw out the match to start their Group F campaign with a win.