Guirassy scores again as Stuttgart close in on Bayern
Guirassy blasted a curling finish into the top corner of the net after 19 minutes to continue his stunning scoring streak this season.
Chris Fuehrich, who has pushed himself into the frame to represent Germany at Euro 2024 after a strong season, added a second after 65 minutes, looping in a long-range effort to double the lead.
Union were reduced to 10 men with 21 minutes left when Andras Schaefer saw straight red for a studs up challenge on Josha Vagnoman.
Stuttgart were boosted on the morning of the game by the news in-demand manager Sebastian Hoeness had extended at the club by two years until 2027.
Hoeness had been linked to a move to Bayern Munich after a piloting the club's remarkable surge from relegation candidates last season to third place in the table.
"It was a deserved victory" Hoeness said after the game.
"We created a lot, but it wasn't perfect," he admitted
Stuttgart now sit third, 10 points clear of fifth-placed RB Leipzig, as they seek a return to the Champions League for the first time since 2009-10.
Guirassy now has three goals in his past two matches. His 21 strikes this season takes him six behind Bayern striker Harry Kane, who has 27 goals in the league having played five more matches.
The loss leaves Union in 14th place, two spots but eight points clear of the relegation placings.
"We had some good opportunities, but you know how football is," lamented Union's Robin Gosens.
"You have the feeling that more was possible."
On Saturday, Bayern can extend the gap on Stuttgart to four points with a win at home to Mainz.
On Sunday, league leaders Bayer Leverkusen can take another step towards a first ever Bundesliga title when they host Wolfsburg.
Xabi Alonso's Leverkusen, who are still unbeaten after 35 games in all competitions, are 10 points clear of Bayern with 10 games to play.