The stalemate leaves Leicester second behind the Gunners on goal difference, completing an amazing turnaround from 12 months ago when the Foxes were bottom of the standings.
After defeat at Anfield on Boxing Day, some questioned the title credentials of Claudio Ranieri’s team but they silenced their critics with another superb performance as they more than held their own against many people’s favourites for the crown.
City stay third and without an away win in the league in six outings since a 1-0 victory at Crystal Palace on 12 September.
The two teams had cancelled each other out, and Leicester had marshalled the threat of Raheem Sterling well, until the 18th minute. It was then that Sterling caught Bacary Sagna’s ball over the top into space and teed up Kevin De Bruyne, whose first-time shot from the edge of the area was parried away by Kasper Schmeichel.
It signalled the start of an assertive spell by City, only briefly interrupted when Aleksandar Kolarov got himself in a tangle and Riyad Mahrez curled a shot narrowly over the crossbar.
City got in down the right again before the half-hour mark following good link-up play between Sagna and De Bruyne. Sterling took a pass on his chest and, losing his balance, hit a volley but Schmeichel got a hand on the ball and it spun past the far post.
Sterling threatened again in the 32nd minute when Schmeichel had to help his left-foot shot from the edge of the box over the crossbar.
Leicester survived the spell of pressure and finished the first half strongly. Four minutes before half-time Vardy was presented with a glorious chance – the type he has buried many times already this season. Fernandinho dallied and lost possession 30 yards out, allowing Danny Drinkwater to put Vardy clear on goal but the Premier League’s top scorer uncharacteristically blazed his shot over the crossbar.
There was more ebb and flow about the second half as chances went begging at both ends.
Sergio Aguero flicked a near-post effort just wide before N’Golo Kante soon had Joe Hart worried with a dipping 25-yard shot.
Marc Albrighton scuffed his shot wide from a good position while at the other end Schmeichel had to push away a Nicolas Otamendi header.
A brilliant pass by Drinkwater gave Vardy another sight of goal but his shot was straight at Hart, who then did well to repel a Fuchs free-kick in the 76th minute.
Both sides had spells of late pressure but neither could make the breakthrough and a draw was a fair result.