Their victory preserved manager Roberto Mancini's perfect start at his new club with a fourth successive win, which was inspired by Tevez who put City ahead after seven minutes, added their third after 49 minutes and scored their fourth in stoppage time.
Micah Richards also got on the scoresheet in the first half with a goal after a surging 70-metre run from the edge of his own penalty area, while Morten Gamst Pedersen replied for unimpressive Rovers after 71 minutes.
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Chelsea lead the standings with 45 points from 20 matches, followed by Manchester United (44 from 21), Arsenal (42 from 20) and City (38 from 20), who moved above Tottenham Hotspur, now fifth with 37 points from their 20 games.
Blackburn, without a league win for nine matches, remained 13th, but are just three points above the relegation zone, having played three more matches than Bolton who are 18th.
City were without striker Emmanuel Adebayor who was with his tragedy-hit Togo team in Africa but he was very much in everyone's thoughts during a minute's silence before kickoff.
The Togo flag was displayed in the stadium as fans and players paid their respects to Togo following Friday's gun attack on their bus at the African Nations Cup in Angola which left two people dead, leading to Togo's withdrawal from the tournament.
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City delayed giving new signing Patrick Vieira (calf injury) his debut although he was given a rousing welcome by the home fans when he was presented to them before kick-off.
Seven minutes into the match City fans were cheering again when Rovers goalkeeper Paul Robinson failed to hold a corner and saw the ball run loose to Benjani Mwaruwari.
He swept the ball back towards Tevez, lurking in the six-yard box, and he turned the ball home off his left thigh for the opener.
They were celebrating again after 39 minutes when Richards doubled their lead.
Richards, who has been linked with a move away from City, powered his way through half the Rovers team in a 70-metre surge upfield before passing to Benjani.
His shot bounced back off a post back into the path of Richards who carried on running and cracked the ball past Robinson to make it 2-0.
Benjani also had an important role in City's third goal, racing past the Rovers defenders before a cut-back intended for Martin Petrov found Tevez instead who gave Robinson no chance from the edge of the box.
Pedersen gave Rovers their one moment to cheer on a bleak night when he scored the first goal City have conceded since Mancini became boss, before Tevez wrapped up the win with an excellent fourth that took his own personal tally to 10 in the last seven league matches and 15 for the season.
The victory could have been even bigger if Tevez had converted a straightforward chance from a header while substitute Robinho had a goal disallowed for offside.
