Although Galatasaray started strongly, they crumbled after Isco made the breakthrough late in the first half as Ronaldo and Karim Benzema feasted on some poor defending.
Gareth Bale started the match on the bench, but came on midway through the second half and created one of Ronaldo's goals.
There was a late consolation for the hosts from Umut Bulut, but it was not enough to bring even a flicker of emotion to the face of disconsolate coach Fatih Terem, who started the night full of hope but ended it with his team in tatters.
Galatasaray started in lively fashion, with Burak Yilmaz testing Iker Casillas in only the second minute, the Madrid captain at full stretch to force his powerful effort away for a corner.
Casillas was starting ahead of Diego Lopez after being told by coach Carlo Ancelotti that he would play in Europe while deputising in La Liga, but his night soon came to a premature end when he took an elbow to the ribs in the 13th minute.
He initially tried to play on with heavy bandaging, but after one attempted clearance he signalled to come off.
Lopez was soon busy too, holding Felipe Melo's close-range header from Yilmaz's free-kick.
Moments later, Madrid appealed for a penalty. Benzema did well to keep the ball in on the touchline before pulling it back to Ronaldo, who tumbled over the outstretched leg of Dany Nounkeu only to see his appeals ignored by Mark Clattenburg.
As play continued, Angel Di Maria curled an effort over the bar.
Galatasaray were still looking threatening, with Wesley Sneijder close to picking out Yilmaz in front of goal after springing the offside trap, before Felipe Melo's superb header was kept out by an equally good save from Lopez.
But it was Madrid who struck in the 33rd minute when Isco's outstanding first touch to Di Maria's long ball allowed him to split the defence and score off the inside of the left-hand post.
Things got worse for Galatasaray when Didier Drogba collapsed under a rough challenge from Pepe just as an already lengthy spell of added time was beginning.
In all, six additional minutes were played, highlighted by a Ronaldo shot parried by Fernando Muslera Drogba failed to reappear for the second half and, without him, Galatasaray struggled to contain Madrid.
Ronaldo's fierce early shot beat Muslera, who needed Nounkeu to hook it off the line, but moments later a defensive mix-up allowed Benzema to run free and finish with ease.
Yilmaz then missed a free header and a chance to put the hosts back in the contest, and Madrid punished him with two quick goals from Ronaldo to end the contest.
Neither was pretty. The first came when Galatasaray failed to deal with Di Maria's cross and Ronaldo was able to rifle home from Isco's knock-back, the second when the Portugal forward lashed home the rebound from a free-kick taken by record signing Bale, on as a substitute moments earlier.
Bale then tested Muslera with a shot of his own which was pushed clear, but it was Benzema who added the fifth, poking into an empty net after Ronaldo drew the goalkeeper from his line before flicking the ball across.
For the Galatasary fans who stuck it out, there was a little something to cheer when the slightest of touches from Bulut diverted Nordin Amrabat's cross into the goal, but Ronaldo had the final word as he completed his hat-trick with a couple of stepovers and a vicious finish as added time began.