Carlo Ancelotti's side made the breakthrough in the 13th minute of the contest, with Rodrygo curling a brilliant effort into the far corner of the net after Vinicius Junior had found his teammate with a clever flick.
Los Blancos were unable to kick on in the first period, though, and Mallorca secured a deserved leveller in the 53rd minute of the contest.
A corner from Dani Rodriguez did not appear to be causing too much trouble inside the Real Madrid penalty box, but Vedat Muriqi came from nowhere to thump a header past Los Blancos goalkeeper Thibaut Courtois and level the scores.
Mallorca had two golden chances to score a second in the latter stages through Antonio Sanchez, but his first effort was just wide of the post, before the attacker struck over the crossbar moments later.
Real Madrid were reduced to 10 men in the latter stages of the fixture, meanwhile, following a poor challenge from Ferland Mendy on Muriqi.
It proved to be a frustrating night for Kylian Mbappe, with the France international failing to build on the goal that he struck on his Los Blancos debut in the UEFA Super Cup against Atalanta BC last week.
In the end, though, Mallorca were well worth their point, with the home side having 11 attempts during a positive performance on the opening weekend of the new campaign.
MALLORCA VS. REAL MADRID HIGHLIGHTS
Rodrygo goal vs. Mallorca (13th min, Mallorca 0-1 Real Madrid)
Real Madrid make the breakthrough in the 13th minute of the contest, with Rodrygo finding the far corner after Vinicius had flicked the ball towards his teammate.
It was a wonderful curling effort from the Brazilian.
Vedat Muriqi goal vs. Real Madrid (53rd min, Mallorca 1-1 Real Madrid)
Mallorca level the scores in the 53rd minute of the La Liga contest, as Muriqi rises highest inside the Real Madrid penalty box to head a corner from Dani Rodriguez into the back of the net.
Muriqi has now scored 28 La Liga goals for Mallorca, and he was not going to be stopped there after wrestling his way past some Real Madrid defenders.
Kylian Mbappe chance vs. Mallorca (70th min, Mallorca 1-1 Real Madrid)
Opportunity for Mbappe to send Real Madrid back into the lead, but the Frenchman's low effort from inside the penalty box is saved by Mallorca goalkeeper Dominik Greif.
It has not quite happened for the France international tonight.
Antonio Sanchez chance vs. Real Madrid (87th min, Mallorca 1-1 Real Madrid)
Sanchez has a big chance to win it for Mallorca, but the attacker fires his effort just wide of the post following a smart piece of attacking play from the hosts.
Ferland Mendy red card vs. Mallorca (97th min, Mallorca 1-1 Real Madrid)
Real Madrid are reduced to 10 men in the final stages of the contest, as left-back Mendy flies into Muriqi and gets absolutely nowhere near the ball.
MAN OF THE MATCH - RODRYGO
Mallorca deserve huge credit for their performance throughout the 90 minutes, but it was a true team display from the hosts rather than any players putting in excellent performances worthy of winning this award.
Rodrygo was the best player on the pitch on Sunday evening, making the breakthrough with an excellent curler into the far corner of the net.
Meanwhile, the Brazilian had two successful dribbles and finished with a pass success rate of 90%, proving to be his team's most productive player on what was a frustrating night for the reigning champions.
MALLORCA VS. REAL MADRID MATCH STATS
Possession: Mallorca 35%-65% Real Madrid
Shots: Mallorca 11-13 Real Madrid
Shots on target: Mallorca 5-4 Real Madrid
Corners: Mallorca 8-7 Real Madrid
Fouls: Mallorca 11-7 Real Madrid
BEST STATS
WHAT NEXT?
Real Madrid will be aiming to record their first victory of the 2024-25 La Liga campaign when they welcome Real Valladolid on August 25, but they will be missing Mendy through suspension due to his red card late on against Mallorca.
Los Blancos will not be adding any more players to their squad before the end of the transfer window, while there will also not be any departures, with David Alaba expected back before the end of the year and Eduardo Camavinga due to return next month.
Mallorca, meanwhile, will look to build on their excellent opening-weekend result when they head to Osasuna on August 24.