With Abu Dhabi's Sheikh Mansour given a standing ovation by the fans on attending his first home game since buying the club two years ago, big-spending City provided plenty for their billionaire owner to savour on a wet night at Eastlands.
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Newly-signed England midfielder James Milner enjoyed an impressive debut, setting up the 13th minute opener by surging into the box and stroking the ball back for former Aston Villa team mate Gareth Barry to side-foot home.
Tevez made it 2-0 in the 52nd, claiming a classic poacher's goal from point-blank range after seemingly adding the final snatched touch to a powerful Micah Richards header.
Richards told Sky Sports television that the goal was his
"It's definitely mine, I'm definitely going to claim it," he said.
There was no doubt about the third, with the Argentine striker calmly sending Pepe Reina the wrong way as he slotted home from the penalty spot in the 68th after Adam Johnson was felled in the box by Martin Skrtel.
City, who have spent more than 100 million pounds on players since they finished fifth last season, moved up to fourth overall after beating Liverpool for the first time since 2005.
Champions Chelsea, who thrashed Wigan Athletic 6-0 on Saturday, have a maximum six points from two games with Arsenal second on four after crushing Blackpool by the same scoreline.
MASCHERANO ABSENT
"The mentality is very important," said City manager Roberto Mancini, who rested new Italian signing Mario Balotelli with Tevez alone up front. "If the squad has a good mentality, it can beat everyone."
It was City's best league result against the once-mighty visitors, whose own title aspirations have been fuelled by the arrival of manager Roy Hodgson and some high-profile summer signings, in 73 years.
"We were a little bit unlucky to get beaten so heavily," Hodgson told Sky. "I didn't think we really deserved to get beaten 3-0.
"Pepe Reina wasn't called into action that often and I thought we had one or two good spells in the game but we were playing against a very effective and strong Manchester city side," he added.
Liverpool were without unsettled Argentine midfielder Javier Mascherano, who is linked to Spanish champions Barcelona, and the suspended Joe Cole but had Spanish striker Fernando Torres - a summer target for City - making his first start of the season.
Liverpool captain Steven Gerrard hit the post with a powerful shot in the second half while City goalkeeper Joe Hart, again favoured over Shay Given, made a stunning double save to deny David Ngog and Torres.
"When Hart made that incredible double save, at 2-1 that might have put some more life back int
