The 14-time major champion dropped three strokes at the opening two holes before slumping to a triple-bogey seven at the 17th.
Woods then produced a delicate chip over a greenside bunker at the last hole and calmly rolled in a seven-foot putt to complete a five-over-par round of 77 and a total of 146, two over.
The 38-year-old American, who won the championship the last time it was held in Hoylake in 2006, is making only his second competitive appearance since undergoing back surgery in March.
"I got myself in good positions to make birdies but didn't make them," Woods told reporters.
Asked about his prospects for the weekend, he said: "It all depends on the weather".
The sun shone all day on Friday, with winds gusting up to 20mph (30kph), but heavy rain is forecast for Saturday's third round.
