Leipzig, who host Manchester City in the Champions League next week, took a seventh-minute lead through Emil Forsberg's shot on the rebound before Sesko doubled the advantage in the 18th, slotting in from close range after a defensive mistake.
The 20-year-old Slovenian, often compared with Manchester City's Erling Haaland for his speed and attacking power, has also netted twice in the league and once in the Champions League in a successful start to his first season in Germany.
But Ivan Prtajin's chip in the 41st got the hosts back in the match with their first chance of the game.
Sesko, who also hit the woodwork late in the game, made it 3-1 in the 70th, before Prtajin scored again, but the visitors held on to win despite some late pressure from Wiesbaden.
The Saxony club have won the last two editions of the German Cup and have played in the last three finals.
