Stuttgart have now gone seven games unbeaten to reach 53 points, nine clear of Borussia Dortmund in fourth and one behind Bayern, both with a game in hand. Bayer Leverkusen lead on 64.
Bundesliga second-top scorer Guirassy put the hosts ahead in the 19th minute with 21st league goal this season thanks to a fine finish at the far post.
Fuehrich doubled Stuttgart’s lead with a superb strike in the 65th and the visitors were down to 10 men four minutes later when Andras Schafer was sent off for a foul on Josha Vagnoman.
The defeat means Union Berlin remain 14th with 25 points, eight clear of the relegation playoff spot.
