Karim Benzema hit the woodwork twice before Nacho and Marco Asensio broke though with goals in the 72nd and 76th minutes respectively.
The win left Madrid 10 points behind Spanish league leaders Barcelona, who visit Getafe on Sunday.
Madrid head to Stamford Bridge on Tuesday holding a 2-0 lead after a convincing first-leg win over Frank Lampard's team in Spain.
"We could have scored more goals, but hopefully we were saving them up for Tuesday," Madrid's former Chelsea goalkeeper Thibaut Courtois said
Carlo Ancelotti once again rotated his squad, with Vinicius Junior and Toni Kroos both staying in Madrid to recover from what the coach described as minor muscle issues that are not expected to keep them from playing at Chelsea.
Luka Modric only played the final 10 minutes, but Benzema - who has missed several games this season with muscle injuries - was in the starting XI.
Cadiz almost caught Madrid off guard in the early stages when right-back Alfonso Espino burst into the area and sliced a shot off the far post but otherwise the visitors dominated.
Benzema wasted a chance from just outside the six-yard box when he fired onto the crossbar in the 35th minute, Federico Valverde shot wide when well placed shortly afterwards and Benzema smacked a second shot off the post midway through the second half.
It finally fell to Nacho, a defender with little scoring pedigree, to surprise Cadiz's in-form keeper David Gil when he fired home from well outside the area after 72 minutes.
Asensio added the second minutes later.
"Nobody could believe (that Madrid had yet to score), but we scored in the most difficult situation, with a shot from long range," Ancelotti said.
"But my team showed energy and motivation in a game that could have been a trap coming just three days before the trip to Chelsea."
Cadiz were left in 15th despite an outstanding showing from Gil.
"In four minutes all the hard work we had put in was ruined," the disappointed goalkeeper said.
Elsewhere, Real Betis moved closer to the Champions League berths with a 3-1 win over Espanyol.
It was a sixth-straight defeat for relegation-threatened Espanyol, while victory lifted Manuel Pellegrini's side into fifth, three points behind fourth-place Real Sociedad who lost 2-0 at Athletic Bilbao.
