The pair had been closely matched in the first set, but a double fault from the eighth seed allowed the Frenchman to get the break on the board before serving out for the lead.
Raonic made a bright start to the second as he looked to get back on level terms, but Simon cancelled out an early break.
However, the 29th seed struggled with his serve a couple of games later to let the Canadian back in front to level the match.
Simon was back on form in the third, saving break points in the opening game before attacking his opponent's serve to clinch the set 6-2, but lost the fourth by the same score as Raonic found another level, taking the match to a deciding set.
The momentum appeared to be with the Canadian as he got the early break, but Simon hit back while the eighth seed was serving for the match.
However, the weary Frenchman could not maintain his intensity, allowing Raonic to get the break back straight away before serving it out of the second time of asking.