It was no more than the Scots deserved after dominating much of the contest, with their goalkeeper David Marshall emerging as the hero when he saved Serbia’s final spot-kick taken by Fulham striker Aleksandar Mitrovic.
Scotland will join the 24-nation tournament’s Group D including England, the Czech Republic and 2018 World Cup runners-up Croatia, with matches in that pool to be played at Wembley and Hampden Park.
Scotland converted all their penalties before Serbia’s top scorer Mitrovic, who had a forgettable night as he was subdued by the visiting defence, aimed a tame shot into the bottom left corner at Red Star’s Rajko Mitic stadium.