The tie was forced to be decided in the fifth set after a four-set tussle which had to be suspended yesterday at the end of play.
The duo resumed today following a tough contest, which started off with both competitors holding their serve well and executing damaging shots across the clay court.
The first set was decided with a tie-break, which was edged comfortable by Granollers who grabbed the one-set lead with a 7-1 score in the decider.
Jaziri became more composed in the second set and managed to take control by retaining his serve and clinching a vital break in the early stages of the set, which proved to be crucial for the 28-year-old, who levelled on sets.
Despite believing that the momentum was in the Tunisian's end of the court, Granollers fought back with a sensational number of forehand shots and returns that led the Spaniard to a 6-1 acquisition in the third set, taking the number 20 seed two-to-one up on sets.
While Granollers looked likely to continue his dominance, the tables turned once more with Jaziri overcoming the pressure and taking the fourth set 6-3 before the end of play.
The duo returned to the court this morning with one set left to play and an equal chance of success for the pair, but it was Granollers who took the early advantage and was able to secure a spot in the next round with a 7-5 victory.