Claude Puel made four changes to the side that faced Tottenham Hotspur last weekend, with the return of striker Jamie Vardy and centre back Harry Maguire providing a huge boost for what would be a tricky test in the capital.
It was Vardy who would force Premier League debutant Vicente Guaita into the first stop of the afternoon as the Spaniard held onto the City No.9’s header at the front post with just over 30 minutes gone.
While there appeared to be nothing to separate the two sides in the first half, Palace went ahead six minutes before the break. Milivojević was given too much space on the edge of the box and the Serbian international had time to find the far corner with a sweet strike.
Puel introduced Rachid Ghezzal in place of James Maddison at the break, as No.7 Demarai Gray moved into a more central position. It was from that area that he had two efforts in as many minutes, but twice fired wide of the mark.
Gray then combined with substitute Ghezzal on 66 minutes, as the former Birmingham City man floated a cross to the back post. Algeria international Ghezzal was there to meet it, but he side-footed off target.
Another huge chance for City followed, but somehow, Guaita kept the ball out. A flowing move saw Vardy fire an effort at goal, only for his shot to be tipped onto the post and the rebound to fall into the arms of the Palace goalkeeper.
Nigeria international midfielder Wilfred Ndidi followed up with an effort with five minutes to play, but his powerful volley soared over the bar, and that proved to be City’s final major effort on goal.
Major moment
With little between the two sides over 90 minutes, few could argue that a draw would have been a fair result at Selhurst Park.
And City came just inches away from sealing that point when Jamie Vardy’s strike hit the inside of the Crystal Palace upright and cannoned straight back to Vicente Guaita.
With a bit of fortune, the back of the net would have rippled, and the Foxes would have returned to Leicester with another Premier League point on the board.
Who impressed?
The introduction of former AS Monaco man Rachid Ghezzal at half-time provided Leicester City with a different kind of forward threat – one that nearly mustered up an equaliser.
The Algeria international fired wide from a Demarai Gray cross midway through the second period, while he was also involved in the move that saw Jamie Vardy’s effort palmed onto the post with around 10 minutes to go.
Where do we stand?
Leicester City drop two positions to 11th in the Premier League standings after their seventh loss of the 2018/19 Premier League campaign. They remain four points off Manchester United in sixth position, but have played one game more than the Red Devils.
Coming up…
Two games against Pep Guardiola’s Manchester City are coming up for the Foxes, either side of a clash with Chelsea at Stamford Bridge.
First, Leicester face Man City in the quarter-finals of the Carabao Cup on Tuesday (7:45pm GMT kick-off) at King Power Stadium before they're back in the capital for a meeting with Maurizio Sarri's men on Saturday 22 December (3pm GMT kick-off).