Cadiz – making his second appearance after arriving on loan from Portuguese giants Benfica – doubled the lead with 17 minutes remaining on Wednesday (AEDT).
Coming off the bench just past the hour-mark after Randall Leal opened the scoring in the 19th minute, Cadiz's long-range shot took a deflection and left Dallas goalkeeper Jimmy Maurer helpless.
Fellow substitute Daniel Rios completed the scoring in the 88th minute when weaved his way past two defenders, sending a scrambling Reto Ziegler to the ground, before firing low beyond Maurer.
The result ensured expansion franchise Nashville earned back-to-back MLS wins for the first time, per Opta.
Of Nashville's 24 points so far, 11 have been won against teams from Texas – seven versus Dallas and four against Houston Dynamo.
Nashville is eighth in the Eastern Conference, while Dallas is sixth in the west following just one win in six games.