Leipzig, one of the favourites to challenge Bayern Munich for the Bundesliga title this season, were always going to provide Union with a difficult initiation.
It was the first time the capital city outfit had conceded four goals at home since November 2014, when they lost 4-1 to 1860 Munich.
Christopher Nkunku, who arrived from Paris Saint-Germain in the summer, scored just three minutes after being substituted on for Germany striker Timo Werner, who also got on the scoresheet. Marcel Halstenberg and Marcel Sabitzer also scored for the visitors, who took a 3-0 lead into halftime.
Union Berlin fans used their debut fixture in the top-flight to stage a 15-minute silent protest aimed at opponents RB Leipzig's ownership by an energy drinks company. Home fans remained quiet for the opening quarter of an hour at the Stadion An der Alten Foersterei as an expression of their opposition to the way Leipzig are run.
Red Bull controls the club in one of the few exceptions to German football's "50+1" principal that members should own a majority of shares. Ironically, the visitors took the lead after 57 seconds through Halstenberg after the Union crowd began to chant for the first time.
Midfielder Halstenberg took advantage of a seemingly unfocused Berlin, curling home while unmarked on the edge of the box. Leipzig coach Nagelsmann said his side were prepared for the boycott and used it to their advantage.
"For a coach it isn't so bad at all - you can talk directly to your players (from the sideline)," he said. "The boys knew that after 15 minutes it would get really loud - and the atmosphere was unbelievably good afterwards. I would always wish that the (Berlin) fans would give it everything from the opening whistle as it's a great atmosphere here at Union - unbelievable."
Leipzig added a second 15 minutes later as heavy rain began to fall, with Marcel Sabitzer punishing Berlin for a defensive mistake inside their own half. Werner added another in the 42nd minute with a powerful strike into the top corner, with the shellshocked home side struggling to keep up with the visitors' talented outfit.
Nkunku's goal in the 69th minute made it 4-0. Union boss Urs Fischer said his team couldn't afford to give teams of Leipzig's quality so many chances.
"When you're playing against a Champions League participant... And you provide so many gifts as we did, you don't need to wonder why the score is 4-0 at the end of the match," he said.