The Spanish giants laid down a real marker of their intent to land a 10th European Cup with a ruthless display of finishing after weathering an early storm in Istanbul.
The visitors stepped up a gear after the break and doubled their lead when Benzema raced through and coolly fired home.
Ronaldo then got in on the act with a close range finish before the Portuguese ace added another when he swept home a rebound.
Galatasaray were in disarray and Benzema notched his second of the game with a two-yard tap-in from Ronaldo's cross.
The hosts grabbed a deserved consolation six minutes from time when substitute Umut Bulut guided into the far corner before Ronaldo completed the scoring with a sensational solo goal in stoppage time.
To cap a good night's work for Ancelotti and co, Gareth Bale came off the bench to make his Champions League bow for Madrid midway through the second period and had a hand in a couple of the goals.
15' DESPAIR FOR IKER - After 238 days out of the team, Casillas' big day comes to an abrupt end after picking up what looks like a stomach injury. Diego Lopez comes on to replace him between the sticks.
17' GREAT SAVE - Free kick to Gala on the far right. Riera whips it in and Melo sees his header fly straight at Lopez who gathers at the second attempt.
33' GOAL - Galatasaray 0-1 Real Madrid. Isco latches onto an exquisite ball over the top by Di Maria and fires a low shot from the edge of the area that creeps in via the post. That goal is very much against the run of play.
48' BIG MISS - Burak Yilmaz guides a simple header wide from just six yards out after a superb cross into the area by Sneijder. It should be 1-1.
54' GOAL - 2-0 to Madrid. Benzema races onto Di Maria's touch after a miscued header backwards by Melo. The Frenchman surges in on goal and coolly doubles Real's lead. A fatal mix up in the midfield for the hosts.
63' GOAL - 3-0 to Madrid. It's game over now. Di Maria rounds the keeper and hangs up a cross that Isco touches back to Ronaldo who makes no mistake from three yards out.
64' BALE TIME - Gareth Bale comes on to make his Champions League debut for Madrid, replacing Isco.
67' GOAL - 4-0 to Real Madrid. Ronaldo snares his second of the game, sweeping in the rebound after Ramos' header from a free-kick was brilliantly saved by Muslera.
81' GOAL - It's five-star Real Madrid. Bale teases a pass into Ronaldo on the left side of the area and the Portuguese ace picks out the run of Benzema who makes no mistake from three yards out.
84' GOAL - Gala get a consolation as Bulut tucks home Amrabat's superb right-wing cross.
90' GOAL - 6-1 to Madrid! Ronaldo hat-trick. Wonderful solo goal from the Portuguese ace, who dances beyond three before crashing a left foot drive into the corner from a tight angle.
Real Madrid have now scored in each of their last 26 Champions League games, the longest current run. The last time they failed to find the net was against Barcelona in April 2011.
Real Madrid have won more games (106) than any other club in the history of the Champions League.
This was Real Madrid's first ever win in Turkey in European competition, having failed to triumph in their previous three attempts.
Ronaldo now has 206 goals in 204 matches for Real Madrid.
TALKING POINT - Just how good can Real Madrid be this season? Cristiano Ronaldo continues to star for the Spanish giants and to score a hat-trick in a 6-1 win in Istanbul is no mean feat by anyone's standards. With a host of stars to come back into the side from injury and a revitalised team spirit under Ancelotti, it could yet be the season when they clinch that elusive 10th European Cup triumph.
MAN OF THE MATCH - Cristiano Ronaldo (Real Madrid): The irrepressible Portuguese ace was in devastating form in the second period, netting yet another treble and a stunning third and final goal of the night.
PLAYER RATINGS -
GALATASARAY: Muslera 6, Eboue 5, Chedjou 6, Dany 5, Riera 6, Selçuk 6, Melo 6, Sneijder 5, Engin 5, Burak 5, Drogba 6. Subs: Bruma 7, Amrabat 6, Bulut 7.
REAL MADRID: Casillas 6, Ramos 6, Pepe 6, Carvajal 6, Arbeloa 6, Khedira 6, Modric 6, Di Maria 8, Isco 8, Ronaldo 9, Benzema 8. Subs: Lopez 6, Bale 6, Illaramendi 6.