The home side started on the front foot, with Antonio Nusa breaking into the area and seeing his low effort saved by Frederik Rønnow.
The Union goalkeeper was called into action for a second time moments later when a ball into the area found Rômulo Cardoso, whose initial effort was well saved before András Schafer did very well to backtrack and head the goalbound ball behind.
Die Roten Bullen maintained the pressure, and they got their reward midway through the first half.
Yan Diomande’s cross from the byline was pushed away by Rønnow, allowing Leopold Querfeld to head away, but only as far as Max Finkgräfe, whose first-time left-footed effort flew into the right side of the net.
Things went from bad to worse for the visitors just three minutes later, when a ball over the top released Cardoso, who capitalised by breaking free and knocking the ball past Rønnow, leaving him the simple task of rolling it into an empty net.
Will Orban’s header came off the crossbar shortly after, shortly before Christoph Baumgartner’s header was brilliantly saved, limiting the deficit to two at half time.
Although Union are unlikely to be involved in a relegation battle, their supporters would like to see them secure their safety sooner rather than later.
However, their cause looked unlikely to be helped in this contest as Leipzig extended their lead just after the hour mark when a clever pass inside the area found Ridle Baku, who wriggled free before sending his effort past the outstretched right leg of Rønnow.
Union managed to get on the scoresheet with their first shot on target in the 78th minute when Danilho Doekhi’s header from a corner beat Maarten Vandevoordt for power, but it proved to be in vain as the hosts reasserted their control, seeing out a commanding win, after surviving a late consolation from Ilyas Ansah that was disallowed for offside.
The result means Leipzig now lead nearest top-four challengers TSG Hoffenheim by eight points with just 12 left to play for, placing them on the brink of securing a seventh top-four finish in the last eight seasons.
Union, meanwhile, remain 11th and six points clear of the relegation play-off place with a potentially nervy end to the season in store.
Flashscore Man of the Match: Yan Diomande (RB Leipzig)