The visitors opened the scoring on the 57th minute when Sergio Aguero emphatically finished off a scintillating City move inside the area.
Their lead was doubled just 84 seconds later - thanks to Ferran Torres - who swept home a left-footed shot from outside the box to put the game out of Palace’s grasp.
Following their 2-1 victory over Paris Saint Germain in midweek, Pep Guardiola rang the changes ahead of the second leg on Tuesday evening – with Ederson, Rodri and Joao Cancelo the only three to keep their place in the starting lineup.
Manchester City kill you with silence. It’s the elegance of how they move the ball, the quiet, yet organised movement that clandestinely patrols the pitch.
It begins with the defence, with Nathan Ake and Ruben Dias orchestrating the tempo, similar to a conductor setting the tone of a musical.
Then the ball reaches Rodri; he subtly brings the game 10-15 yards forward and sets up the attacking prowess that has crept forward.
Benjamin Mendy and Joao Cancelo wait in the wings, while Gabriel Jesus, Raheem Sterling and Sergio Aguero pincer inside the box, bewildering defenders.
It’s a tactic which Roy Hodgson’s side set up for, sitting in a deep 4-5-1, and for the first 15 minutes, Palace looked well equipped to match the constant Manchester City bombardment.
But City fought back.
A long ball allowed Sterling to bemuse Cheikhou Kouyaté and Joel Ward, dragging the former to the ground and setting himself up for a one-on-one - but Tyrick Mitchell tracked back to snatch the ball off Sterling’s feet to block a certain goal.
But it was a move Pep Guardiola would have been proud of himself that nearly allowed Benteke to open the scoring.
He spotted Ward, who had galloped in the box, and Ward drilled the ball across the face of goal - it created instant confusion, allowing Benteke to poke a shot towards goal and forcing Ederson into another save.
After a tetchy 20 minutes, Jesus thought he put the visitors in front when he met a Ferran Torres cross in the box, but VAR ruled the goal out for offside.
Jairo Riedewald was the catalyst in Palace’s next attack - driving forward with the ball down the left-hand side and setting up Eberechi Eze outside the penalty area. But, unfortunately for Eze, his left-footed shot drifted wide of Ederson’s post.
With the second half in full swing, the intensity of the game rose.
Ferran Torres drifted between Mitchell and Kouyate. As he collected the diagonal ball, he clipped it over Guaita, destined for the back of the net – but Dann had other ideas, heading it off the line to keep Palace’s clean sheet intact.
However, the defensive resilience was short-lived.
Manchester City nonchalantly spread the ball around the pitch, with Mendy collecting it just over the halfway line.
He looked up and spotted Sergio Aguero darting into the box.
The ball evaded everyone in red and blue, falling at the feet of Aguero, who took one touch and emphatically smashed the ball into the back of the net.
Their lead was doubled on the 59th minute.
Shocked into submission, Palace allowed City to attack with real verve, venom and vigour.
Ferran Torres picked up the ball on the edge of the box and curled a left-footed shot into the bottom left-hand corner, out of Guaita's reach to effectively kill off the game.
City should have had three. Raheem Sterling crashed a shot off the post and Aymeric Laporte’s header was cleared off the line by Benteke.
Palace were motionless, lost for any form of movement.
However, City’s stubborn defence blocked the Eagles when they pushed forward.
City moved 13 points clear of Manchester United, with the Premier League title in touching distance.
As for Palace, they stay 13th and very much entrenched in mid-table obscurity.