The visitors enjoyed a dominant first half in which they created the best chances, and they may have felt aggrieved not to have gone in ahead at the break.
While Hazard wasn't having the best game of his career, fans were well aware of the fact that he remains the main source of creativity for Chelsea.
Chelsea's fourth successive draw in all competitions could see them slip to fourth by the end of the weekend, while Leicester will take heart from a thoroughly deserved point at Stamford Bridge.
Antonio Conte had been wary of the Foxes and his concern proved well founded as the movement and energy of Riyad Mahrez, Jamie Vardy and Shinji Okazaki troubled Chelsea.
The second half picked up where the first half left off, as Chelsea continued to look off the pace in the games.
When looking to the bench, Conte did not have the players required to change the game despite Willian and Pedro coming on as Morata once again struggled and Cahill's injury took up one of their options.
If anything, in retrospect view of Ben Chilwell's 68 minute second yellow, the presence of Hazard could have been the decisive factor in ensuring that the game went in favor of the Blues.
Wilfred Ndidi's header was kept out by Thibaut Courtois at full stretch before Aleksander Dragovic was denied on the follow-up, while Kasper Schmeichel spread himself well to block Cesc Fabgregas' attempt from a narrow angle moments later in what was an already open encounter. "We just have to keep working and keep trying to win every game". They had 12 first-half shots, the most for an away side at Chelsea in well more than a decade according to Opta, and Puel will have been disappointed that his side weren't leading at the break. The Algerian threatened Chelsea's backline most of the times when he rushed forward, but lack the output today.
Andreas Christensen replaced him in defence, but Conte does not expect the skipper to be ruled out long term.
A second booking in the space of five minutes for Chilwell meant Leicester had to play out the final 20 minutes a man light, and the Blues could not make their numerical superiority count.
Morata managed just three touches in the opposition box all game - his worst return from a completed Premier League game this season - while only four completed crosses from 19 attempted illustrated the wayward service on offer.
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