A second goal from Marko Vejinovic 10 minutes from time had put Vitesse on course for a fourth straight league win before Tighadouini completed his own brace late on.
Vejinovic opened the scoring with a 32nd-minute penalty after Isak Ssewankambo committed a foul in the box.
The visitors had a golden opportunity to equalise before the break, but Erik Falkenburg missed a spot kick of his own.
They were on level terms just after the hour mark, though, when Tighadouini scored his first goal in seven games, but Vejinovic took his own tally for the season to five to restore Vitesse's lead on 80 minutes.
The hosts were on their way to second in the table, but Tighadouini equalised for Breda again to prevent them from suffering a fifth defeat in six games, although they remain 16th in the table.