The 26-year-old from Portugal looked down and out when she slipped on the turf while falling a double-break down at 4-0, and Williams wrapped up the first set in just 27 minutes.
But the 2002 and 2003 champion lost focus early in the second, with her forehand especially error-prone, and Silva grew in confidence as the set progressed, saving a break point to move to 4-4.
Williams was not to be denied though, and after netting a backhand on her first match point in game 10 a heavy return did the job two games later.
Asked if her concentration had slipped or Silva had improved in the second set, Williams said: "A little bit of both. I definitely think she increased her game, but also I think my concentration on some key points, it wasn't where it should have been.
"And, you know, it's just a point here or there that can make or break a match."
Williams said last month that she considered herself the real number one as Safina has yet to win a Grand Slam title, but she backed the Russian - who has never been past the third round at Wimbledon - as the top seed this fortnight.
"I think Dinara should be the number one seed," said the American. "She's been really consistent the last couple months. She's earned that number ranking."
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