Etherington free kick found the net from the edge of the area on the hour
Premier League side Stoke had to come from behind against non-league York to reach fourth round of the FA Cup.
York took the lead when Neil Barrett headed Alex Lawless's free-kick in.
But, within two minutes, Danny Parslow then deflected Rory Delap's throw into his own net, and then Stoke scored again inside 60 seconds.
Ricardo Fuller headed in the second from close range after another Delap throw and Matthew Etherington made sure with a curling free-kick on 58 minutes.
The opening exchanges of the tie, which was delayed for 30 minutes after the York team bus became stuck in traffic on the M62, were relatively even despite the supposed gulf in class.
Michael Rankin had York's first chance but shot well wide of Sorensen's goal and soon after Parslow's attempted clearance hit Fuller on the back and looped over the defender but into the side-netting of Michael Ingham's goal.
But the game sprung into life midway through the first period with an incredible three goals in the space of four minutes.
And it was the Blue Square Premier League visitors who shocked their hosts with a goal from midfielder Barrett after 22 minutes.
Fellow midfielder Lawless whipped in a free-kick from the left flank and Barrett glanced a near-post header across Sorensen's goal and into the far corner of the net.
But a few moments later York's 4,000 travelling supporters were left feeling deflated when Parslow turned Delap's powerful long throw-in into his own net.
Neil Barrett celebrates his first-half opener after giving York the lead
Shortly after, Stoke went ahead after a Delap throw-in again caused mayhem in the York defence and Fuller was on hand at the back post to head down and in from three yards out after Leon Cort teed him up.
And just before the break panic ensued again after another Delap throw, with Levi Mackin almost sending the ball past Ingham for a second own goal, but the Minstermen survived.
Sorensen was replaced at half-time by Steve Simonsen who was called into action early in the half by the lively Richard Brodie whose turn and shot was comfortably held by the Stoke keeper.
Minutes later Ingham was also called into action superbly tipping defender Robert Huth's shot behind for another Stoke corner.
But just before the hour, Stoke put the tie to bed when winger Etherington found the top corner of the net with a free-kick from the edge of area after James Meredith had fouled Fuller.
Stoke boss Tony Pulis: "We didn't think they would get here in time.
"We are so set in our pre-match routines that it does set you back.
"That was probably a factor in us only springing to life after their goal. But the way York battled was a credit to them."
York manager Martin Foyle told BBC Radio York: "People said we should have come down overnight but we set off at 10.15, which was ample time to get here.
"It was one of those days when everything happened against us. We arrived at three o'clock but we are not using that as an excuse.
"Stoke were great about it and the referee was fantastic and organised.
"We played a game of football and I'm not looking at that as an excuse.
"The players had half an hour to warm up. Yes, it's a little bit of a panic, but look on the bright side - they didn't have time to think about it, go out, look at the pitch and start worrying about Stoke City.
"I think Tony Pulis would say we were organised and hard to beat. And, although we defended them very well in training, on the day the trajectory of Rory Delap's throws are frightening, It's a missile that could keep Stoke in the Premiership again."
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