Snapped up after last season's treble-winning exploits with Inter Milan, Mourinho's arrival as coach at the Bernabeu has raised expectations he can end Barcelona's two-year reign as champions.
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While his new team were struggling to click in Mallorca, Pep Guardiola's well-drilled outfit banged in three goals thanks to Lionel Messi, Andres Iniesta and David Villa.
Real Madrid's Argentine striker Gonzalo Higuain was denied three times by home goalkeeper Dudu Aouate and Cristiano Ronaldo spurned a great chance as the visitors upped the pressure.
Mourinho's new signings Mesut Ozil, Sami Khedira, Angel Di Maria, Sergio Canales and Ricardo Carvalho all featured but despite a frantic finish Michael Laudrup's Mallorca were worth their point.
"We are a team in construction. I would like us to have had three points... but it's not a dramatic situation," Mourinho told reporters. "On a positive note we conceded very few chances and had no problems at the back.
"The negative point is the result. I'm disappointed that with the number of chances we created we didn't score.
"When you aren't at your best you have to do two things, defend so your opponents don't score, and take your chances. We deserved to win," added Mourinho.
"We were good tactically and very good in defence," Real Madrid's keeper and captain Iker Casillas told Spanish television.
"We did well and little by little will get better. The ball just did not want to go in."
Barca had earlier thrown down the gauntlet, appearing unruffled by the contentious exit of Zlatan Ibrahimovic to AC Milan.
DELIGHTFUL LOB
Messi, who grabbed a hat-trick in the Spanish Super Cup last weekend, only needed four minutes to rip open the defence and score with a delightful lob.
Iniesta followed up with a volley from outside the area and new signing Villa headed his first league goal in a Barca shirt, after Victor Valdes had saved a penalty before the break.
"We still lack a little continuity in our play but this will improve as the season progresses," Guardiola told reporters.
Second division champions Real Sociedad celebrated their return to La Liga after a three-year absence with a 1-0 win at home to Villarreal.
Xavier Prieto raced on to Joseba Llorente's backheel to score after 57 minutes, making them the only promoted club to win in the opening round of matches.
Levante and Hercules were beaten on Saturday.
A double strike from Pablo Osvald
