Zinedine Zidane's men were held by Valencia before the international break and Lucas Vazquez's first-half response was only enough for another tie upon the resumption of the league.
Such was Real's frustration at their inability to break down Levante's stubborn defence -- marshalled superbly by goalkeeper Raul -- that wing-back Marcelo saw red at the death.
The home defence, with Sergio Ramos returning, fell asleep in the 12th minute when Ivan Lopez's long throw-in evaded them all to find Ivi, who just needed to stick out a leg and poke the ball home.
The Valencians could not put further daylight between themselves and Real, though, and Vazquez's equaliser in the 36th minute dampened their spirits after a bright first-half showing.
Real's bid to snatch a late winner suffered a blow when Marcelo lashed out to earn a red card. Toni Kroos almost cut through the gloom to clinch it when he rattled a post deep into stoppage time.
Zidane faces further fall-out from the draw at home to Levante, with Karim Benzema set to be sidelined for around a month with a thigh muscle injury.
Benzema underwent hospital tests after the game, with the club releasing a statement saying he had suffered a hamstring injury, which AS reported would see him sidelined for four to six weeks out.
Valencia and Atletico Madrid both protected their unbeaten records but will have been frustrated by their goalless draw at the Mestalla.
Diego Simeone's Atletico enjoyed the better chances to force the issue, with Angel Correa and Luciano Vietto going close in the first half before Nicolas Gaitan was denied on the hour mark.
With time ticking away, Martin Montoya missed an opportunity to clinch it for Los Che as Jan Oblak parried his effort from the middle of the box.
Sevilla dominated Eibar at the Sanchez Pizjuan to win 3-0 and record back-to-back victories.
However, it took the Andalusians until the 46th minute to score, with Ganso rifling home Nolito's assist at the expense of Eibar goalkeeper Marko Dmitrovic.
Sevilla continued to turn the screw and Wissam Ben Yedder continued his hot streak in front of goal by tapping in a Pablo Sarabia cross. At the death, Nolito rubber-stamped the result at the far post. PLACE YOUR TEXT ADVERT BELOW:>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> How I Made Me =N=2.5 MILLION In 7 Days from 2 Common Product I Imported and how you can do the same. Click HERE FOR FREE Details right now Warning To Men: This 3 Foods Is Killing Your Erection. Click Here To Know Them This Simple Trick Will Reverse Your Diabetics Within Few Days