Third seed Raonic lost the first set against Briton James Ward, but recovered to claim a 5-7 6-3 6-2 success.
Ward regularly pressured Raonic's serve in the first set, which he served out to love after registering his sole break of the match.
But Raonic's class told as he turned the match around to set up a second-round clash with Richard Gasquet.
Gasquet needed just 56 minutes to see off Simone Bolelli 6-1 6-2.
But there was no joy for former world number one Hewitt - who will retire after the 2016 Australian Open - at a tournament he has won four times in his career.
The Australian succumbed 6-7 (5-7) 7-5 6-2 to Kevin Anderson, who fired down 22 aces on his way to victory.
Defending champion Grigor Dimitrov was halted by bad light in his match against Sam Querrey, with the scores tied at one set apiece.
American Querrey took the opener 6-4 and secured an early break in the second, but Dimitrov reeled off five games in a row from 3-1 down to level it up.
Elsewhere in the draw, Fernando Verdasco overcame Roberto Bautista Agut in three sets and Guillermo Garcia-Lopez claimed a straight-sets win over Pablo Andujar in two all-Spanish contests.