It wasn't straightforward for Chelsea as initially anticipated because Leicester made known their presence in the game.
Jose Mourinho's team struggled right from the first half to break down Leicester City,failing to hit a shot on target.
The chances that came their way in the first 45minutes,both Diego Costa and Andre Schurrle hit over the post.
Leicester on their part were confident,passing the ball without fear and they even had a shot on target that Thibaut Courtois did well going down to make a save.
Chelsea had two chances in a space of thirty seconds as they pressed to carve Leicester open.
Oscar came close in the 47th minute,curling in a shot from the edge of the box that bounced off the post.
Moments later Cesar Aziplicueta hooked in a cross that met Branislav Ivanovic's head,but Kasper Schmeichel made a spectacular save.
Ivanovic thundered in another shot from outside the box which Schmeichel did well yet again to keep out.
By then Chelsea were getting into their strides and having a strong foothold in the game.
However it was Leicester who came closest to find the net,quickly breaking play and setting off on a counter attack.
David Nugent was played through on goal and in a one-on-one situation,Courtois showed why he has been installed as the first choice keeper,making a superb save to keep out Leicester when it looked almost certain that the ball was going into the net.
That miss did hurt them as Chelsea were made to be aware of the danger they were in if they fail to take their own chances.
Cesc Fabregas tried an ambiguous chip but Schmeichel was equal to it.
However the Dane was finally beaten when a great work by Oscar set Ivanovic in motion and the Serb with a brilliant dummy laid the ball in the paths of Costa who finished off the move to put Chelsea 1-0 up.
Eden Hazard made it 2-0 and it was vintage Chelsea who ended the game winners after finding a way to beat Leicester.
Chelsea as was expected did the job,but they were caught out by Leicester who exposed them a bit.
With the win,Chelsea are the early season leaders,topping the table with maximum points after two matches.
Aston Villa 0 - 0 Newcastle
Chelsea 2 - 0 Leicester
Crystal Palace 1 - 3 West Ham
Southampton 0 - 0 West Brom
Swansea 1 - 0 Burnley