Trailing 4-3 at one stage, Carter stormed back and rattled off a 106 break to take the opener of the final session before edging a scrappy second.
Woollaston had his chances in the third which went down to a black ball game but again Carter proved stronger under pressure and booked his place in the second round with an assured clearance of the colours after Woollaston squandered a healthy lead.
O’Sullivan now awaits and he is a player Carter knows well, having fallen at the final hurdle against the reigning four-times world champion in the 2008 and 2012 finals.
"It wasn't the best performance but it's all about getting through these matches," said Carter. "Ben played very well in the first session so I was delighted to be 5-4 up. And then to win the final five frames was the icing on the cake.
"I'm not buying into the fact that Ronnie hasn't played in a competitive match because he's probably fresher than all of us and rest assured he's been practising very hard for this tournament. If a marathon runner hadn't done an ounce of training and turned up to do the London marathon and won it, then I'd be pretty impressed. But if he'd been doing all the training before, just because he's got people running next to him then does that make any difference? Not in my book.
"Ronnie's played out of his skin against me a lot of the time. I've played him in a lot of high-profile matches and he's never thrown in a bad performance. We've practised together over the years so he knows how good I am."
Ben Woollaston kept pace on his Crucible debut with twice-finalist Ali Carter, just one frame down at 5-4 after a tight first session.
An epic opening frame which lasted 39 minutes eventually swung Carter's way after the two-time finalist showed his defensive qualities.
But Woollaston responded by clinching another slow, cagey frame. The 25-year-old from Leicester left Carter needing snookers and eventually sealed the frame with a fluke on the pink.
But there was nothing fluky about the next frame as Wollaston, cueing brilliantly at times, raced into a 3-1 lead before the interval, only for Carter struck back with a silky break of 84 to close to within a frame of his opponent.
Woollaston hit back with a break of 48 at the start of the sixth frame, but it wasn't enough as Carter clawed his way back and levelled at 3-3.
Woollaston stopped the rot to re-establish his lead, but Carter compiled a near flawless break of 96, before edging the final frame of the session to hold a narrow 5-4 lead.
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