Joint third with Paul Casey and Lee Westwood on six under par overnight, the 27 year old ended it two over, but realising how lucky he was.
"Not many people play the Saturday of The Open," he said. "I made the cut. It could have been worse - I could have been packing my bags."
Returning to the 11th tee at 6.30am as one of 30 players unable to finish their second rounds on Friday night, Tiley double-bogeyed it and then dropped five more shots for a 79 that saw him survive the axe with only a shot to spare.
"I just couldn't make a par," said the Kent golfer. "I tried my hardest, but the last eight was panic really.
"After a couple of three-putts I suddenly couldn't stop making bogeys however hard I tried. That's just golf - when it goes it goes."
He had gone to bed at 11pm, but "tossed and turned" until his alarm clock went off at 4am - and then had to be driven to the course by a friend when his courtesy car failed to arrive.
Teeing off again at 10.50am he added a 73 and, while no longer in contention, he had the thrill of a birdie at The Road Hole 17th.
"I had a chat with my coach before the round and the emphasis was on enjoying it and forget about what happened, steady the ship and get my confidence back," he said.
"That was one of the longest days of my life and I need some sleep, but I can't wait for tomorrow."