Lucas Vazquez cancelled out an early Ivi Lopez strike to leave the two teams on terms ahead of the second period, but Real could not find a second as they dropped home La Liga points for the second successive match.
A positive start from the home side saw Karim Benzema work a shooting chance inside the opening three minutes, but Levante midfielder Jefferson Lerma was across at the vital moment to make a brilliant last-ditch challenge.
It was all Real Madrid in the early moments, but Levante took a shock lead in the 12th minute of action when Ivi beat Dani Carvajal to a bouncing ball inside the Los Blancos box before finishing past Casilla.
The champions came on strong, with Asensio having a goal-bound shot blocked moments after the opening goal went in, while Benzema and Marcelo were also causing problems with their movement in the final third.
Benzema had to be replaced in the 28th minute after picking up an injury while stretching for a loose ball, however, and an under-pressure Bale was introduced as Real Madrid looked to level the scores against a well-drilled Levante outfit.
Ivi actually came close to doubling Levante's lead just past the 30-minute mark after trying his luck from a 30-yard free kick, but the attacker's effort, which almost caught Casilla at his near post, hit the side-netting.
Real Madrid did level the scores in the 36th minute, however, when Vazquez tapped home from close range after Levante goalkeeper Raul Fernandez had palmed a header from Ramos straight into the path of the Spain international.
Zinedine Zidane's side came close to taking the lead late in the first period when Bale met a super cross from Marcelo, but the Welshman's header dropped wide of the post, before Fernandez kept out the former Tottenham Hotspur attacker in a one-on-one situation moments later.
Real Madrid made a fast start to the second period, but Levante remained a threat in the final third, and Casilla had to get down to keep out a low strike from Alex Alegria in the 50th minute during an end-to-end period of the match.
Bale had another super chance for Real Madrid just before the hour after Vazquez found the Welshman with a cross from the right, but the attacker's header was too high, and that prompted another change as in-form Isco entered the field.
Asensio was next to try his luck as the Spaniard curled one wide of the far post 20 minutes from time, before Carvajal stung the palms of Fernandez in the 74th minute as the score stayed 1-1 in the Spanish capital.
Fernandez made another smart save to keep out Asensio in the 82nd minute, before Bale headed an excellent chance wide of the post once again in the 87th minute as the Welshman's struggles continued.
Real Madrid were then reduced to 10 men in the 88th minute when Marcelo picked up a straight red card for kicking out at Levante defender Pedro Lopez after the Brazilian had seen an effort saved by Fernandez.
Kroos almost won it for the home side in stoppage time, but the German saw his curling effort hit the outside of the post as Levante continued their impressive start to the season with a point in the Spanish capital.
Next up for Real Madrid, who could be four points off the top of the table later tonight, is a home game against APOEL in the Champions League on Wednesday night, while Levante will look to continue their unbeaten start to the season when they host rivals Valencia next weekend.