Guirassy double as Dortmund down Monterrey to reach Club World Cup quarters
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.
"I think I could have scored at least three goals but I am happy to have helped the team win," Guirassy told broadcaster DAZN.
"I expect a very tough game. Real Madrid want to go through so it will be a tough game but we will be prepared."
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.
"Guirassy is one of the best strikers in the world," Dortmund's Yan Couto told reporters.
"Today he scored two goals and he made the victory."
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 with a couple of chances when he might have netted a third.
"I think I could have scored at least three goals," admitted the striker.
Ramos comes close
Monterrey, who earned an impressive draw against Inter Milan in the group phase, were dangerous going forward but Dortmund goalkeeper Gregor Kobel stayed alert to keep Corona at bay before the break.
The Swiss stopper could do nothing about Berterame heading home a looping rebound from close range early in the second half as Monterrey came out forcefully.
Kobel made another solid save to thwart former Porto star Corona, who appealed in vain for a penalty when he felt he had been shoved over from behind by the hulking Niklas Suele as he ran through.
Berterame did beat Kobel but the goal was ruled out for offside, with the noisier portion of the 31,000 attending left groaning.
Guirassy snatched at another chance to complete a hat-trick on a rare Dortmund forray forward as Monterrey fans chanted "yes we can".
The Mexican side's supporters were also warned late in the second half over discriminatory chanting, for yelling a word considered homophobic when Kobel took goal-kicks -- the Mexican football federation has been punished by FIFA in the past over the same issue at international games.
As the clock ticked down Torrent threw Ramos up front, desperate for some last-gasp magic from the 39-year-old.
Sporting the number 93 on his back, harking back to his famous 2014 Champions League final goal for Real Madrid to deny rivals Atletico, the Spaniard came inches away with a header in stoppage time which dropped agonisingly wide.
"The crowd and our fans and the people who understand about football, they saw that the team gave everything," Ramos told DAZN.
"Our supporters, I think they are proud of how we defended the shirt, and we have to continue moving forward."