Watson finished with a par 71 and handed the lead to Des Smyth, who shot 70 and held the clubhouse lead with a 2-under 140 total for more than six hours at windswept Muirfield. No player broke 70 on Friday.
'I left my putt short, about five feet and then I missed it,' said Watson, who has won this event twice. 'Not a good way to end.'
A five-time British Open winner -- including on the same Muirfield links in 1980 -- Watson was tied for second with Eduardo Romero (71), Gordon J. Brand (73) and Stewart Ginn (70) at 1 under. Faldo shot a 74, two strokes behind the leader after opening with a 68 Thursday in his senior tour debut.
'Although I shot 3 over, I felt as though I was making bogey everywhere,' said Faldo, winner of six majors, including three British Opens. 'I am still in it so, if I can find something and get the right attitude, then who knows what can happen.'
Watson, whose four birdies were spoiled by four bogeys on the back nine, also left a 30-foot eagle putt at 17 on the edge of the hole. But one of his shots from a fairway bunker at 14 struck a spectator on the head.
'I pull-hooked it out of the bunker way left of the green,' Watson said. 'Nobody saw it and, boom, it hits him on the head and comes all the way across the green and leaves me with actually a pretty easy chance for bogey, which I made.'
Watson beat Smyth in a playoff at the 2005 Senior British Open at Royal Aberdeen and that's the closest the Irishman has come to a major on the senior tour.
'Obviously, I would love to win,' he said. 'But, whatever happens, I need a good result because I am worried about keeping my card. I need a big result somewhere along the line and this could be the place to do it.'
A strong wind blowing across the Muirfield links led to some high scoring and whittled away at the scores of the first-round leaders.
Playing into the wind, however, Faldo sliced his second shot into the rough well short of the green. Although he was close to reaching par with a 20-foot putt, it rolled to the left of the cup and he made bogey to surrender his lead.
Renowned for making par after par under pressure, Faldo didn't make one in the first five holes. They were a mixture of three bogeys and two birdies, and at one stage he had fallen four behind Brand, who was co-leader overnight.
But Faldo pulled himself back into contention for a share of the lead only to leave a putt for eagle 3 feet short at the 17th and then missed again.
Nick Job, one of three players tied with Faldo for the first-round lead at 3 under, carded an 85 to miss the cut, which was 9 over.