Ward looked on the brink of defeat after losing the first set, but the world number 169 fought back to win 4-6 6-4 12-10.
Rola, the number four seed, broke Ward's serve twice during the opening set, but the Londoner responded in the second to take the match into a decider.
Ward looked in control of the third after moving a break of serve up, but after missing a match point his opponent, who is ranked 94 in the world rankings, broke back to make it 5-5.
With the set needing to be won by two games, both men held serve with relative ease before Ward broke in the 21st game to give himself the chance to win a place in the main draw at Roland Garros for the first time.
The 27-year-old had let nerves get the better of him earlier in the set, but he held serve to 15 to become the first British male to come through the qualifying rounds for more than 40 years.