In a game of limited clear chances, a deflected effort from Aurelien Tchouameni early in the second half proved the difference for Los Blancos, who built towards a defining period of the campaign next week in the UEFA Champions League and hosting Barcelona in El Clasico.
With an eye on next week’s European quarter-final second leg against Manchester City, Madrid manager Carlo Ancelotti opted for five changes, but England midfielder Jude Bellingham retained his place in the side.
The visitors made a bright start, with Luka Modric sending an early free-kick straight into the wall.
Mallorca, recently beaten in the Copa del Rey final by Athletic Club, was proving difficult to break down.
In the 34th minute, Bellingham sent in a curling effort from the edge of the penalty area but it looped over the goalkeeper and cannoned off the crossbar.
Madrid finally made its pressure count three minutes after the restart.
Tchouameni picked the ball up around 25 yards out before drilling in a rising drive which took a deflection off a Mallorca defender and spun off up into the top right corner.
Brahim Diaz had a chance to quickly double the lead after running into the Mallorca penalty area but his effort was straight at goalkeeper Predrag Rajkovic.
As the hour mark passed, Mallorca substitute Abdon Prats saw his shot blocked before Real missed the chance to add a second.
Modric cut a pass back to Diaz just outside the six-yard box but the winger’s touch was too strong, which allowed Rajkovic to kick the loose ball clear.
Ancelotti then made a couple of changes, with Diaz and Bellingham given a rest as Vinicius Junior and Eduardo Camavinga were sent on.
Madrid pressed for another goal to kill off the match, with Camavinga playing in Federico Valverde, only for his effort to be hacked off the line by Mallorca defender Matija Nastasic.
Sergi Darder almost scored a fine equaliser when his 25-yard effort, flying towards the top left corner, was palmed away by Real keeper Andriy Lunin at full stretch.
With 10 minutes left, Joselu’s header from a free-kick was saved by Rajkovic.
Mallorca almost snatched a dramatic equaliser with what proved to be the last kick of the game deep into stoppage-time.
Lunin jumped with Vedat Muriqi as he tried to catch a high cross into the Madrid box but dropped the ball, which the Kosovo striker then stabbed wide of an open goal.
