One break of serve is all that separated the two players during the opening set. World number 20 Simon was the player who managed to claim it and in doing so ensured he took the set 7-5.
An early break of Hanescu's serve soon followed in the second set to give 27-year-old Simon the advantage.
He pressed home his domination to eventually emerge as a 6-3 victor.
Simon will now take on Japan's Kei Nishikori for a place in round four.