Nordstrand swept the ball home from the spot nine minutes after the break as the Danish champions did only what was required to make a winning start to the group stage.
Visiting Vorskla fashioned few decent chances and barely deserved to take anything from the game, the Ukrainians lacking quality in the final third and too anxious to pull the trigger when in sight of goal.
After Ahmed Januzi missed with an early chance for the visitors, it was Copenhagen, perennial campaigners in Europe, who settled much the quicker to their task.
With 14 minutes on the watch Nordstrand forced Vorskla goalkeeper Serhiy Dolhansky into the first save of the match, while Dolhansky then held from Thomas Delaney's header as the hosts continued to make all their early running.
Vorskla's ineffective tactic of shooting from distance first reared its head on 32 minutes, Oleksiy Kurilov taking aim from 30 yards with a shot that was always fading right.
Dame Ndoye headed wide for the hosts on 33 minutes, while Vorskla's optimism continued to get the better of them with Ahmed Januzi and Roman Bezues both wayward with long-range efforts either side of the break.
Cristian Bolanos flashed a shot wide for the hosts from just outside the area on 50 minutes as Copenhagen continued to look the most likely to break the deadlock.
The game-deciding penalty arrived on 54 minutes, Oleksandr Matvyeyev the offending party with a foul on Johnny Thomsen in the area. Nordstrand stepped up to take the kick and had no trouble beating the goalkeeper with a shot into the bottom-left corner.
The visitors struggled to break down the organised Copenhagen defence after falling behind, with the Danes competently shutting up shop at the back.
Only one further chance went the way of the visitors before the final whistle, and once again it was from long range. This time, at least, Johan Wiland was forced into action in the Copenhagen goal, although it was no more than a routine stop from Oleg Barannik's 25-yarder.