Djokovic, the second ranked player in the world, is off to a slow 2014 and has only defeats at the Australian Open and the Dubai Duty Free Championship to show for thus far.
He failed to reach the final in either event, but does bring positive vibes to Indian Wells, California where he is a two-time champion.
Facing the Romanian Hanescu, Djokovic fended off five break points during the competitive opening set before dominating the tiebreaker and taking complete control of the match from there.
"I didn't make any returns in the first set. (In the) Second set I also struggled with the return, which is one of my better sides in the game generally speaking," Djokovic told reporters after registering his 550th career win, the sixth active player to do so.
"It's the first match and it takes a little bit of time to get used to the center court. I haven't played on it this year."
Djokovic will next face Alejandro Gonzalez who made the third round by defeating Ivan Dodig 6-4 2-6 7-6.
British number three James Ward went down 3-6 6-2 6-4 to Feliciano Lopez.
Ward took a lucky loser spot after sixth seed Juan Martin del Potro withdrew due to a left wrist injury that had also forced him out of the Dubai tournament last week.
However, the Brit took only one of his 10 break point opportunities as he went down in three sets against the world number 37.
Elsewhere in the draw, a couple of high seeds were sent home packing early.
Berdych had been in strong form, winning 11 matches in a row in February, but slipped up in the early loss.
Ninth seed Jo-Willfried Tsonga, of France, also bowed out in a 6-4 6-4 loss to fellow countryman Julien Benneteau.
Eighth seed Richard Gasquet and 12th seed John Isner advanced after surviving a volatile day.
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