The Argentine scored a brilliant hat-trick to make it ten goals in his last seven Premier League appearances and 15 for the season as City overpowered Blackburn Rovers at Eastlands to climb into the fourth Champions League place.
City, despite being without Africa Cup of Nations pair Emmanuel Adebayor and Kolo Toure and a number of other injured players, were still far too strong for an out-of-form Rovers side which is now without a win in nine league matches and worryingly close to the foot of the table.
Mancini, who has won all three league matches and an FA Cup tie at Middlesbrough, was vindicated in his decision to prefer Benjani to expensive Brazilian Robinho in the starting line-up.
The hard-working Benjani, making his first league appearance of the season, provided assists for the first three of City's goals and deserved praise for a valuable contribution to City's cause.
City made a seventh-minute breakthrough when Rovers keeper Paul Robinson's poor punch from Martin Petrov's corner was turned back across the face of goal by Benjani for Tevez to divert the ball into the net off his knee from inside the six-yard box.
The goal from Tevez was very much in keeping with most of the opening period which was a scrappy, disjointed affair.
But six minutes before the break City doubled their advantage through Micah Richards' third goal of the season.
Richards made a thrilling run from well inside his own half before slipping the ball to Benjani whose shot struck an upright only for central defender Richards, who remained upfield, to slot the rebound into the empty net.
Rovers made a double substitution at the break bringing on front pair Nikola Kalinic and David Hoilett, but any hopes of a second-half fightback were ended when Tevez scored his second and City's third goal less than four minutes later with a sweetly-struck shot following a Benjani cut-back.
City conceded their first goal under Mancini in the 71st minute when Vincent Kompany's failure to control a chipped clearance from keeper Shay Given allowed Morten Gamst Pedersen to curl in a delightful consolation goal.
Tevez, fittingly, had the final word completing his first treble for City in stoppage time when he curled in another exquisite shot from the edge of the box.