Real at one stage led 5-1 during the tie, however defensive errors in the return leg in France enabled the home side to claw their way back into the game, thanks largely to the superb Ludovic Giuly despite Raul opening the scoring,.
Both sides began in attacking fashion with Patrice Evra surging down the left flank while at the other end Roberto Carlos's shot was inches away from Raul in the box.
Monaco thought they might have had a penalty claim after 14 minutes, however referee Pierluigi Collina pointed for a corner when Roberto Carlos tackled Giuly in the box.
Captain Giuly was a constant thorn for the Madrid giants, but after his first effort was blocked on the edge of the box he followed up his shot by pulling the rebound wide.
Iker Casillas was forced into a dramatic save minutes later when Fernando Morientes's sweetly struck shot was arrowing into the top corner, but the Spanish international palmed it to safety.
Just when it looked like Monaco had the edge, the visitors burst away at the other end and scored the goal that put Real in firm control of the tie.
Ronaldo raced towards Monaco's box before passing to Guti, who cleverly dummied the ball allowing Raul to hit a first time effort past the helpless Flavio Roma.
It was a landmark goal for the 'Golden Boy' with his 237th strike for the club pushing his total past Ferenc Puskas in the club's all-time goal-scoring charts.
Raul continued to cause problems, but with Roma's goal in sights, his well-struck effort was blocked by Gael Givet to give the visitors a left wing corner.
With half time approaching the home side got their foot back in the door when the lively Giuly connected with Morientes's knock-down to drill a right-footed effort past Casillas.
The visitors failed to show up in the early part of the second half with Monaco maintaining their momentum from the opening 45 minutes with Morientes putting the home side ahead.
The Spanish international, who is on loan from Real and scored in the first leg, connected with Evra's superb left wing cross leaving Casillas no chance in goal.
Jaroslav Plasil tried his luck from range shortly after, but his left-footed effort sailed well over the visitors' goal.
Real could have been further behind moments later, but Morientes failed to apply the killer touch at the back post with only Casillas to beat.
Monaco's remarkable comeback was completed after 66 minutes when Hugo Ibarra's dangerous right wing cross was touched home from close range by Giuly.
The French international was inspirational on the night for the home side and in scoring two goals almost single-handedly dumped out their illustrious counterparts.
Real thought they had retaken the aggregate lead late on, but Raul's excellent header that nestled into the bottom corner was ruled out due to offside.
Shabani Nonda, on as substitute, almost completed a personal comeback, after a lengthy spell on the sidelines, but his close-range header bounced over Roberto Carlos and crashed against the post.
Real failed to pull the goal back that would have taken them through into the semi-finals of the competition causing one of the biggest upset in the tournament this season.
