The win, which broke the record of 11 games set in the 1955-6 season, put the champions three points clear with 37 from 16 matches. Second-placed Osasuna, who have 34 points, visit fourth-placed Real Madrid at the Bernabeu on Sunday.
Winger Ludovic Giuly set Barca on their way with a well-taken 31st-minute strike and Cameroon striker Samuel Eto'o scored from the penalty spot just before the break.
Eto'o grabbed his 15th goal of the season four minutes into the second half and Cadiz keeper Armando then produced some fine saves to prevent the score climbing higher.
Cadiz striker Nenad Mirosavljevic netted a deserved consolation goal in the final minute.
Barca coach Frank Rijkaard said: "It was very difficult to play against Cadiz because they played at such a high tempo.
"But every part of the team continues to work well. We are organised and we were able to manage the ball well, so I want to congratulate my players for an important victory."
Deportivo Coruna had earlier moved up to third on 29 points by humbling regional rivals Celta Vigo 3-0 away.
Celta had goalkeeper Jose Manuel Pinto sent off after only 24 minutes for bringing down Pedro Munitis in the area and Diego Tristan scored from the penalty.
Playmaker Juan Carlos Valeron skipped past three challenges to score a second goal after 42 minutes and three minutes later defender Joan Capdevila lashed a free kick home from 25 metres.
Diego Tristan also put a second half penalty wide.
Athletic Bilbao continued to pull away from the foot of the table with a comfortable 2-0 win at home to bottom side Real Betis, who have not won in nine league outings.
Perhaps missing the influence of Brazilian playmaker Ronaldinho, who was ill, and the injured Xavi, Barca struggled against a fired up Cadiz early on.
But after 31 minutes Andres Iniesta set Giuly through on goal with a sliderule pass and the Frenchman lifted the ball over the advancing Armando for the opening goal.
A minute before the interval Rafael Marquez won a penalty for the visitors when he dived over a sliding tackle from Cadiz defender Jose de la Cuesta in the area.
Eto'o was forced to take the penalty twice but sent Armando the wrong way second time around.
Soon after the restart Deco squared the ball across the area for Eto'o to shoot but Armando parried at full stretch. Lionel Messi collected the loose ball and pulled it back for Eto'o who scored from close range.
To their credit Cadiz never lost hope and in the final minute a quickly taken free kick allowed Mirosavljevic space in the area to stab past Victor Valdes.