The Welshman sent a left-footed free-kick into the net midway through the first half after Cristiano Ronaldo had opened the scoring with a thunderous strike from over 30 yards out.
Karim Benzema then widened the scoreline even further before the break, taking advantage of a fine move from Luka Modric, and in the second half Angel Di Maria scored his second goal in as many games before substitute Alvaro Morata piled further misery on Liga whipping boys Betis.
Real coach Carlo Ancelotti remarked: "The team played with quality and were focused throughout the match.
"We had a lot of chances and the support given by the midfielders, especially Modric, was very good."
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