The former world number one missed The Masters and the US Open earlier this year and is playing for only the second time since undergoing back surgery in March.
His return to Hoylake, where he won the last of his three Open titles in 2006, started well on Thursday as he shot a three-under-par round of 69 to sit three behind Rory McIlroy at the top of the leaderboard.
However, he could not repeat this performance in the second round as he dropped three shots on his opening two holes.
He would par his way to the 17th, where he drove out of bounds and ended up making a triple-bogey seven to fall to three-over-par - one shot under the projected cut line at the Royal Liverpool club.
The 14-time Major winner ensured that he would continue into the weekend, though, when he got up and down from the side of the 18th green to make birdie and avoid missing consecutive cuts for the first time in his career, despite a five-over par round of 77.