City went into the break level despite taking an early lead but Aguero's four second-half goals saw the Blues cruise home to move 16 points clear at the top.
For Aguero, it was another chapter written into his stunning City career.
City, with two changes from last weekend’s draw with Burnley, signalled intent straight from the kick-off with six players ready to sprint forward on the halfway line.
And with barely two minutes completed, Sterling put the Blues ahead.
Bernardo drew in two defenders on the right before playing a pass to Kevin De Bruyne who had time to look up and whip in a trademark low cross that Sterling met at the far post for his 20th goal of what has been a prolific campaign.
City continued to dominate with some lovely, free-flowing football against the Foxes, though many moves fizzled out in or around the edge of the box.
The Foxes had offered little or no threat going forward but a series of misplaced passes saw the ball fall to Jamie Vardy and the England man skipped past two challenges before drilling a low shot past Ederson with possibly a slight deflection off Aymeric Laporte’s challenge.
City responded quickly with Bernardo and Fernandinho forcing decent saves from Kasper Schmeichel and De Bruyne’s low drive brought another good stop from the Dane.
Sterling’s appeal for a penalty was waved away by referee Mike Jones and though replays showed Wilfred Ndidi has caught him slightly, it would have been harsh on the Foxes.
It was open and entertaining stuff from both sides.
Four minutes before the break the visitors had an excellent clearance from Aleksandar Dragovic to thank for preventing Sterling doubling his tally for the evening as the City winger poked the goalwards after skipping past Schmeichel.
Though the Foxes had pegged back the Premier League leaders in the opening 45 minutes, the Blues shifted up a couple of gears after the re-start to quickly put the game out of Leicester's reach.
It was the same combination on each occasion that undid Claude Puel's men with the first coming on 49 minutes starting with Sterling's pass to De Bruyne and his sumptuous low cross was turned in by Aguero at the far post.
Within four minutes the Blues had clear daylight as De Bruyne played a simple ball to Aguero and the Argentine span away and tucked home a low shot that Schmeichel couldn't keep out.
That was 26 for the season for Sergio and a hat-trick of assists for the brilliant Belgian.
But the prolific Argentine wasn't finished.
As Leicester tried to find a way out from the back, Schmeichel's casual pass was intercepted by Aguero who sent a sublime chip over the Dane to complete his twelfth City hat-trick for the Blues.
And in the final minute Sergio capped a memorable display with a thumping shot from 20 yards that struck the underside of the crossbar to send the Etihad wild.
Terrific stuff from City.
De Bruyne's excellent cross just after the break restored confidence and belief as well as setting the tone for a super second-half.
Star man: Aguero
Who else? Though De Bruyne's hat-trick of assists pushed him close!
What it means…
City go 16 points clear of Manchester United who play tomorrow afternoon against Newcastle United.
City travel to Switzerland on Tuesday for the Champions League Round of 16 first leg with FC Basel.
Then there is a six-day break before the Blues take on Wigan Athletic in the FA Cup 5th round at the DW Stadium.