Mahrez finally returned to training on Friday and it seems he has been welcomed by his teammates and the Leicester fans as well as Puel.
Sergio Aguero scored his second hat-trick in three home games since the club called off their move for Alexis Sanchez.
Sterling made immediate amends for a glaring miss last weekend.
After going behind within three minutes, many teams would have folded but Leicester hung in there.
Leicester had levelled in the game when Jamie Vardy picked up Kyle Walker's wayward pass and converted with a clever run and finish, but it proved to be only one of two shots on target in the contest.
He had two possible penalty shouts in either half while he nearly came close to scoring a second in the 41st minute.
Sterling went close to a second just before the break as he beat Schmeichel only to be denied by a fine block from Aleksandar Dragovic.More news: (NASDAQ:MSFT) Position Lifted by Sunbelt Securities Inc
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Kun Aguero then completed his hat-trick after a horrific error by Leicester goalkeeper Kasper Schmeichel lost control of the ball and presented the ball to the City frontman, who delightfully dinked the ball over the onrushing goalkeeper to seal an emphatic 4-1 lead for Pep Guardiola's side.
It's a stunning and vital personal contribution in a season when City keep breaking records.
One positive for the Foxes was the return of winger Riyad Mahrez, who played just under half an hour in place of Fousseni Diabate.
But just to make sure Aguero pounced on a disastrous clearance from Schmeichel and chipped the Dane in nonchalant fashion. Aguero unleashed a rocket of a shot from just outside the box in the 90th minute to score his fourth goal of the second half.
"We felt we could have stopped a couple of their goals today, because they were our fault".
"Now we have Champions League, and the [Carabao Cup] final, so important games".
When asked about his favourite goal of the game, he added: "I don't know, maybe the last one because it's a long time since I scored from outside the box".
Belgian star Kevin De Bruyne provided three assists for City in the win.