The score means Luxembourg sit in third place in Group A with 6 points and a game in hand, while Serbia go top of the group with 14 points. Portugal are hot on their heels, however, with a game in hand to come against Luxembourg, where they will be hoping to bolster their tally of 13 points.
The Red Lions put on a strong performance on Saturday, hoping to make up for their previous 4-1 defeat away to the Serbs, but it was not to be. Luc Holtz's team had an abundance of chances to even out the game, dominating the first half, but they fell frustratingly short as Vlahovic scored the winner for the away team in the 68th minute.
Elsewhere in Group A, Ireland beat Azerbaijan 3-0, putting them in fourth place.