Sergio Aguero scored his second hat-trick in three home games since the club called off their move for Alexis Sanchez.
Pep Guardiola’s men now need just 20 points from their remaining 11 matches to be crowned champions and the chances are it will be less.
Kevin de Bruyne’s super curling cross from the right wing and there was Sterling to tap in at the back post to tap in his 20th of the season.
Sterling was in almost exactly the same spot as when he missed the sitter at Burnley last week – clearly he has learned his lesson during a few days in the sunshine.
After going behind within three minutes, many teams would have folded but Leicester hung in there.
And midway through the first half they were level after a loose pass from Nicolas Otamendi into the path of Jamie Vardy.
The England forward survived a couple of heavy tackles as he made his way to goal before planting the ball past Ederson Moraes via a deflection off Aymeric Laporte.
For the second time in a week, City had let a lead slip after doing the same at Turf Moor seven days ago.
Then Sterling danced round Schmeichel but his effort from narrow angle was turned behind by Aleksandar Dragovic.
Pep Guardiola may have had some stern words with his team because they had the game wrapped up within 10 minutes of the re-start.
First Sterling swapped passes with de Bruyne before the Belgian rolled over a cross for Aguero to score at the back post.
And five minutes later he was there again, latching onto another pass from De Bruyne before firing a shot which Schmeichel could not hold.
The former City keeper would have been disappointed he didn’t keep it out.
Aguero didn’t care though as he celebrated a 26th goal of the season – and made it 195 goals now for City. The double century will not be long.
Just after the hour, Foxes boss Claude Puel threw on Mahrez – but it felt like the game had already gone.
But just to make sure Aguero pounced on a disastrous clearance from Schmeichel and chipped the Dane in nonchalant fashion.
And to make matter even worse, he netted his fourth of the evening in spectacular fashion in the 90th minute after his blistering drive from distance cannons off the underside off the bar and over the line.