Tchouameni's powerful effort just after half-time took a slight deflection before it flew high into the net.
With one eye on their trip to the Etihad, Real boss Carlo Ancelotti took the opportunity to rest and rotate players.
The result was a slightly scrappy performance as Mallorca made life difficult for Los Blancos.
The contest was settled by Tchouameni's shot from 35 yards which skimmed off the leg of Manu Morlanes and gave Mallorca goalkeeper Predrag Rajkovic no chance.
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