The striker scored twice in the first half and Bundesliga powerhouses Dortmund then held off the Mexican side in a battling second after German Berterame’s quick strike.
Former Real Madrid great Ramos had a golden chance to equalise at the end but headed wide, meaning it is Dortmund who go on to face the Spanish giants in the last eight after they beat Juventus earlier on.
After grinding through several games in the blazing afternoon sun during the group stage, Dortmund were grateful to be at the air-conditioned Mercedes-Benz Stadium and played at a faster pace in Atlanta.
Monterrey coach Domenec Torrent warned his side they had to defend diligently to have a hope of beating Dortmund, but the Germans picked the locks too easily to open the scoring in the 14th minute.
Guirassy exchanged quick passes with Karim Adeyemi on the edge of the box to confuse defender Jorge Rodríguez, and then tucked a slick finish home at the near post.
The 29-year-old Guinea international, who finished as joint-top scorer in the Uefa Champions League this season, netted his second 10 minutes later.
Jesus Corona came close to levelling by accident in between, but his cross bounced back off the post.
Guirassy climbed to 37 goals for the season across all competitions as he was once more teed up by the darting Adeyemi, stroking home from the edge of the box.
Dortmund coach Niko Kovac anticipated Monterrey playing with aggression but his side put in the harder tackles in the first half and Jobe Bellingham was booked for needlessly flying in on Colombian playmaker Nelson Deossa.
It means he will not be able to face his older brother Jude Bellingham in the quarter-final showdown against Real.
Guirassy let Monterrey off the hook when he might have netted a third and Adeyemi’s touch was loose when he got in behind. (AFP)