The five-time world champion booked his place in the next round with a 10-4 victory over his Finish opponent.
Hull is ranked 122 in the world and has only appeared at this tournament once before, yet O'Sullivan insists he just wants to take it one game at a time.
"I'm just pleased to have got through," 'The Rocket' is quoted as saying by BT Sport. "I don't really see there's a massive expectation on me.
"I'm just here to do a job and I go about it as professionally as I can. There's one out of the way and I just move on to the next."