Milner, a 26 million-pound capture from Aston Villa last week, set up Gareth Barry's coolly-taken opener on 13 minutes.
Carlos Tevez was credited with City's second and his 50th EPL goal, although replays suggested if he did divert home Micah Richards' towering header he applied the faintest of touches.
"It was definitely mine, I am going to claim it," Richards said after the match.
There was no doubt about the Argentina striker's claims to the third, though: it came from the penalty spot after Martin Skrtel had felled Adam Johnson.
The emphatic margin of victory will have thrilled City's long-suffering fans and Arab owner Sheikh Mansour, who was watching his first game at Eastlands almost two years to the day since buying the club.
Since taking over 24 months ago Mansour has ploughed in almost 350 million pounds on new players and another 200 million in off-field improvements. On this showing his outlay could finally bring an end to a barren run of 34 years without a trophy for the blue half of Manchester. Victory took them fourth, just below their arch cross-city rivals United.
"I think it was a fantastic night for Manchester City, I am very happy," Mancini said. "We played with only Tevez in front, but if the squad has the right mentality you can beat everyone."
Mancini side-stepped questions about the title, adding: "I think it's important to improve game by game. We need time to gel and become a strong squad."
While City's fortunes appear to be on the up, problems continue to mount for Roy Hodgson and Liverpool.
Not only has a proposed takeover failed to materialise, it looks as though midfielder Javier Mascherano may have played his last match for the club. The Argentina midfielder was left out of the visitors' 18 despite being fit, with some reports suggesting that Barcelona had tabled a bid of 12 million pounds.
Reds boss Roy Hodgson said: "Obviously there's some speculation about his future and his mind is not right so it was correct not to select him. Hopefully things will be resolved, certainly before the end of the transfer window.
"I would like Mascherano to stay. That's my wish, that's my hope. We don't want to sell him, and certainly not for the type of fee that's being suggested at the moment."
Hodgson added: "We were a little bit unlucky to get beaten so heavily but we were playing against a very effective and strong Manchester City side and of course they scored their goals at just the right time."
While Milner was handed his City debut, but there was no Premier League bow for Mario Balotelli, Mancini choosing to rest the former Inter Milan striker after he picked up a knee injury in Europe.
City escaped with a goalless draw at Spurs last week after barely managing a shot on goal, but they only had to wait 13 minutes for their first league goal of the season.
Johnson slipped the ball though for the unmarked Milner and he pulled the ball back for Barry to sweep the ball into the corner.
Even with Spain striker Fernando Torres restored to the starting line-up Liverpool looked short of ideas and their best effort of a disappointing first half came when captain Steven Gerrard sliced wide.
City doubled their lead early in the second half, with Tevez claiming he got the final touch after Richards had outjumped Daniel Agger to thunder a header goalwards from Milner's corner.
Liverpool came close to pulling a goal back five minutes later when Gerrard crashed a shot against the post from outside the area. Joe Hart preserved his second clean sheet of the season with superb reaction saves to deny David Ngog and Gerrard on the follow-up.
Johnson had been impressive on the right side of a City front three and he tricked Skrtel into a clumsy challenge to give Tevez the chance to add a third from the spot on 67 minutes.
Courtesy of Score Mobile FC (http://www.thescore.com)\n
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