Sterling saw his strike turned in by Alex Oxlade-Chamberlain after the restart and both sides could- and should - have added more in the time that remained.
Nobody in sky blue was complaining, however.
The guard of honour completed; it was clear even in the warm-ups that this was a game both teams desperately wanted to win.
And within the first ten minutes there could have been a couple of goals, with City seeing a Gabriel Jesus effort narrowly ruled out for offside and Mo Salah forcing Ederson to push the ball out and then gather Firmino’s weak follow-up.
Salah went close again on 19 minutes with a low shot from the edge of the box that struck the foot of the post as City rode their luck again.
But on 24 minutes, Raheem Sterling received the ball in the box, turned Joe Gomez whose close attention eventually brought the City forward down to give ref Anthony Taylor a simple decision to point to the spot.
Our new penalty king De Bruyne coolly sent Alisson the wrong way to put City 1-0 up.
Liverpool continued to look dangerous and Ederson’s excellent anticipation as Fabinho played Salah clear was crucial as he slid into a clearance and then followed it up by clearing into touch of Jordan Henderson’s toes.
City continued to find space behind the Liverpool midfield and on 34 minutes, it lead to a second goal as Phil Foden, De Bruyne and Sterling poured forward, De Bruyne was the decoy as Foden found Sterling who took one touch before rolling the ball past Alisson from close range.
And in first-half added time, it got even better.
While City had been ruthless up front, Liverpool had been wasteful with their opportunities and that was the main difference as the teams went in at the break.
Liverpool continued to fluff their chance – a couple the result of a few stray passes by the City back-line – until the fourth goal finally killed the contest off.
Mahrez had one scrubbed off for a baffling VAR decision with the last kick of the game (Foden penalised for hand-ball) and City had to settle for four, but with superb performances all over the pitch - Sterling in particular - this was a satisfying victory.
Foden seems to raise the bar each time he plays and, against the meanest defence in the country, he scored one, made another and forced Alisson into a fine save – as well as having another shot cleared off the line.
De Bruyne was everywhere, a shining beacon of excellence and invention, scoring one and was heavily involved in two more.
These are two of the players Pep Guardiola will build his team of 2020/21 around.
Subs: Bravo, Stones, Zinchenko, D Silva, Doyle
Liverpool: Alisson, Alexander-Arnold (Williams 76), Robertson, Van Dijk, Gomez (Oxlade-Chamberlain 46), Fabinho, Henderson, Wijnaldum (Keita 52), Mane (Minamino 85) Salah, Firmino (Origi 62)
What it means…
City move within five points of securing a Champions League berth, while reducing the gap to leaders Liverpool to 20 points.
City travel to Southampton to face an in-form Southampton at St Mary’s Stadium.
The game kicks off at 19.00pm BST and will be shown live on BBC 1.