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The world number two got the better of his 32-year-old opponent 7-6(1) 6-2 in their second-round encounter in one hour and 24 minutes.
Hanescu started the contest on a positive note and took Djokovic down to the wire in the opening set, before eventually losing 7-1 in the tie-breaker.
The 26-year-old Serbian then stepped up his game in the second set and surged to a 3-0 lead.
Despite Hanescu trying his best to stage a comeback, Djokovic maintained his momentum, winning 29 points overall and two of his five break points to clinch it 6-2.