Karim Benzema added a second on the half-hour mark with a looping header into the corner, before the Frenchman doubled his personal tally with a scrappy goal shortly before the break.
Here, Sports Mole takes an in-depth look at a significant 90 minutes at Anfield.
On target: 2
On target: 7
Was the result fair?
Absolutely. Liverpool started the match brightly, pressing Real Madrid with great gusto and unsettling the defending champions, but as soon as that level of intensity dropped then Real Madrid's quality began to shine through. After the opening 20 minutes they took complete control of the game, and didn't let go until the final whistle.
Every Madrid player seemed to have an extra yard of space as Liverpool began to sit off, and with the likes of Toni Kroos, Luka Modric and Ronaldo pulling strings, that is only going to lead to one thing. It was a ruthless 18-minute spell in the first half when Madrid took the game beyond Liverpool and ended it as a contest before the break.
It was a fairly low-key second half, with Los Blancos happy to see out the victory and Liverpool knowing that they stood very little chance of clawing their way back into it. Madrid controlled it very comfortably and could have even added to their lead. Liverpool had a few chances of their own during the game, but the three-goal margin does not flatter Madrid whatsoever.
It all started so promisingly. Spurred on by a raucous Anfield crowd, Brendan Rodgers's side came out of the blocks quickly and were competing with everything. They more than held their own against the star-studded Madrid outfit in the opening stages, but there was no way that they could keep that level of intensity up for the full 90.
Indeed, it waned after just 20 minutes, and from that moment on Liverpool were comfortably second best. Madrid controlled the ball, dictated the tempo of the match and simply didn't give Liverpool a way back into it. Even so, Rodgers will be unhappy that his side gave away two goals that could have been avoided.
The first strike was a moment of magic from Ronaldo, but both of Benzema's goals came from Liverpool once again not dealing with high balls into the box. The Reds did fairly well not to collapse and make it embarrassing in the second half, as it looked like it could go that way at one point, but they were simply outclassed and beaten by the better side tonight.
Real Madrid's performance
They were forced to weather an early storm, but in the end this was a classy, composed and comfortable victory for Real Madrid. They came into the match having never won or even scored against Liverpool in three previous meetings, but given their recent goalscoring form that was never a record that was going to continue tonight.
Once they took control of the game, they looked a class apart from the hosts. They made very few mistakes in possession and ruthlessly put Liverpool to the sword in the first half. The first two goals were finishes of the highest order, and in truth they should have had a few more after the break.
There was an element of complacency that perhaps crept into their game in the second half, but in many ways it was the perfect match for Madrid ahead of their showdown with Barcelona on Saturday. They had the game won by half time and were in cruise control after the break, never in danger of letting the lead slip. They really are a special team, and it would not be a surprise if they became the first side to retain the trophy in the Champions League era.
Sports Mole's man of the match
Cristiano Ronaldo: A number of players would be worthy winners of this award tonight. Benzema's good performance was rewarded with a brace, while Kroos and Modric controlled the game from midfield. As so often is the case, though, it was Ronaldo who shone brightest.
His first goal was a thing of beauty as he clipped a volley past a helpless Mignolet, while he was a constant threat all night, with Liverpool struggling to get near him. In truth, he probably should have broken Raul's record of 71 Champions League goals tonight, but that seems to be only a matter of time for a man in such scintillating form.
Madrid's third goal was a very messy one, and there has to be serious questions asked about the Liverpool defence. All of them got dragged underneath the ball, which flew over their heads to Pepe, who poked it to Benzema to finish. It was shambolic defending from the Reds, who seem incapable of coping with set pieces at the moment.
Nicola Rizzoli is as experienced as they come right now, and he kept a good level of control over the game. A couple of his decisions drew the ire of the Anfield crowd, but he did not make any howlers and only went to his book once all evening.
Liverpool: Liverpool return to domestic action looking to make it three Premier League victories in a row when they host Hull City at Anfield on Saturday.
Real Madrid: Madrid, meanwhile, face one of their stiffest test of the season as bitter rivals and La Liga leaders Barcelona arrive at the Bernabeu for El Clasico.