Jose Mourinho turned to reserve team players Alvaro Morata and brothers Alex and Nacho Fernandez who all started in a side that also featured experienced internationals such as Ricardo Carvalho and Michael Essien.
Among the players left in Madrid for the trip to the 'Segunda B' side were Iker Casillas, Pepe, Sergio Ramos, Xabi Alonso, Mesut Ozil and Cristiano Ronaldo but it made little difference as the visitors controlled the game from the beginning.
Benzema headed home a long ball from understudy goalkeeper Antonio Adan on 20 minutes for the opener before Kaka doubled the lead before the interval with a left-footed strike.
Seventeen-year-old substitute Rodriguez curled home a right footed shot for the third on 66 minutes to make it a dream debut for the youngster.
Five minutes later Javi Lara got a deserved consolation for the home side direct from a free-kick.
However Benzema was able to walk through their tired defence and score with two minutes remaining and the team from the Alicante area face an uphill task in reversing the result in the Santiago Bernabeu in the second-leg.
Earlier joint La Liga leaders Atletico Madrid won 3-0 in their first-leg tie at 'Segunda B' side Real Jaen, who played with ten men for 65 minutes after Dani Torres was sent-off.
Diego Costa with a penalty, Adrian and Raul Garcia got the goals that mean the return leg should be a formality for Atletico in the Spanish capital.
Third placed Malaga were made to suffer before clinching a 4-3 win at Cacereno, while top rung side Celta Vigo suffered a shock 2-0 defeat at second division Almeria.
Rayo Vallecano also lost to lower league opposition, 1-0 in Las Palmas, and have it all to do in the second leg.