Billed as another showdown between Real's Cristiano Ronaldo and PSG's Zlatan Ibrahimovic, it was instead 19-year-old Rodriguez who settled the contest with a low right-footed finish in the 19th minute after being played in by Alvaro Morata, who has been linked with Arsenal.
Real head coach Carlo Ancelotti occupied the same role with the Parisians last season and could claim one over on his former club at the Khalifa Stadium, yet the sense of it being an exhibition game was inescapable, with the Spanish club changing their entire starting XI at half-time, meaning Ronaldo played for only the first 45 minutes.
Ibrahimovic came off midway through the second half.
As with Sweden's World Cup play-off against Ronaldo's Portugal, Ibrahimovic was on the team that came off second best.
Real resume their campaign in Spain's Primera Division on Monday, when they tackle Celta Vigo.
Paris St Germain's first game after the French winter break comes on Sunday against Brest in the Coupe de France.