Levante, who didn't include Socceroos goalkeeper Mitch Langerak in their matchday squad, took the early lead via Ivi's surprise opener before being cancelled out by Lucas Vazquez.
But ultimately, it was another difficult 90 minutes for the champions at the Santiago Bernabeu, as they handed Barcelona another early boost in the title race.
Zinedine Zidane's side drew 2-2 with Valencia prior to the international break and they were once more unconvincing as they failed to take all three points against last season's La Liga winners, with Marcelo sent off for a petulant kick in the dying minutes.
Madrid handed first starts of the 2017-18 season to Theo Hernandez and Marcos Llorente, with Isco, Casemiro and Gareth Bale all on the bench and Luka Modric and Keylor Navas rested entirely after their exploits for their national teams, while Cristiano Ronaldo remained sidelined through suspension.
Zidane had stressed the importance of utilising his squad prior to the match but they looked well short of their best against a disciplined visiting side, who kept Madrid restricted to half-chances after Vazquez levelled after Ivi's early goal.
Karim Benzema picked up a suspected hamstring injury and Marcelo saw red late on to compound a poor outing for the home side, who will be four points behind Barca after only three games if Ernesto Valverde's side win the derby with Espanyol later on Saturday.
The half-full-looking Bernabeu crowd were stunned when Levante took the lead after only 12 minutes, Ivi pouncing on a loose ball and lifting it over Kiko Casilla after the Madrid defence failed to deal with an Ivan Lopez long throw.
Matters got worse for Madrid when Benzema hobbled off after slipping when controlling the ball, forcing Zidane to throw on Bale after only 27 minutes.
Frustrations were starting to build but the hosts drew level 10 minutes before the break, Vazquez tapping home after Raul Fernandez had just kept out a header from Sergio Ramos, who was back from suspension.
Bale glanced a header narrowly wide but should have done better two minutes later, the Wales international breaching the offside trap but failing to beat Raul from inside the penalty area.
The Wales forward nodded over another presentable chance before Zidane decided to try to force the initiative and introduced Isco from the bench just past the hour mark.
Madrid's control of possession did not let up but the end product in attack was becoming increasingly erratic, with Marco Asensio slicing wide after a good run and Dani Carvajal sending a cross from a promising position straight into Raul's gloves.
The Levante keeper endured a nervy moment when he spilled a Carvajal volley before gathering but he produced the save of the match to deny Asensio from inside the penalty area with only eight minutes left.
Bale missed another headed opportunity as Madrid poured forward in the dying stages, but it was far too little too late from the European champions ahead of the start of their Champions League defence next week.
Marcelo forced another fine save from Raul but was promptly sent off for kicking out at Jefferson Lerma as he attempted a block before Toni Kroos struck the post in stoppage time, leaving Zidane with plenty to ponder ahead of a busy month to come.