The 26-year-old will next face Stanislas Wawrinka who beat Tomas Berdych 6-3, 4-6, 6-4.
World number 113 Andujar was blown away in the opening set, winning just nine points, as Nadal broke three times to take it 6-0.
Victory extended Nadal's incredible run to 31-2 since returning from the tendinitis problem in his knee.
He is a huge favourite to win his third title in Madrid after a week of surprises which saw exits for the world's top three ranked players, Novak Djokovic, Roger Federer and Andy Murray.
Berdych is in fine form at the moment having won on clay in Portugal last weekend.
<Center><b><i>Copyright AFP (Agence France-Presse), 2013</b></i></center>