Daniel Msendami netted the winner late in the first half at the Marbella Football Center on Saturday night.
Ibon Sanchez had opened the scoring after just four minutes before an 11th minute Tshepang Moremi leveller.
The Buccaneers kicked off their Spanish tour with a 1-1 draw with Cordoba.
Head coach Abdeslam Ouaddou made wholesale changes for this tie and handed a debut to young defender Christian Derbyshire.
They endured a difficult start against the Segunda Division side with Sanchez following up his goal with another good chance that he put wide of the target.
But Moremi got Bucs back in the game as he connected to a good corner from Captain Deon Hotto.
Boitumelo Radiopane should have done better in front of goal in the 38th minute but he ballooned his shot over the bar.
Msendami though was well placed to finish a pass from Moremi to ensure the Buccaneers ended the half in the ascendancy.
Ouaddou rang the changes at half-time but his well-drilled Pirates team continued to impress, with Neo Rapoo the closest to a third goal with his powerfully hit free-kick, while Cadiz best chance after the break fell to Antonio Cordero in the 66th minute but he blazed over.
Pirates next face Saudi side Al Ittihad on Tuesday 21 July.
The Soweto giants will then play Segunda division club Las Palmas on 22 July before wrapping up their tour against Saudi side Neom SC on 24 July.