The 35-run victory against Sunrisers Hyderabad was Bengaluru's second win in nine matches
The victory was marred by the sight of Barca talisman Lionel Messi, making his first start of the season, receiving lengthy treatment for a blow to his thigh in the first period before being replaced at halftime by Ousmane Dembele.
Antoine Griezmann headed Barcelona in front after six minutes, darting in at the near post to meet a Messi corner.
However, Cazorla's long-range effort left home keeper Marc-Andre ter Stegen red-faced as he misjudged the swerving shot to allow the visitors back into the game before Barcelona held on to move up to fourth with 10 points after six games.