Williams came back from a 15-40 deficit with some precise ground strokes, before clinching the contest with an angled ace.
In front of a near capacity crowd, the world No 10 took a while to get going.
She had to fight hard in her second service game, fending off a break point, as she tried to find her groove. There were some sweetly struck shots, mixed in with a few mishits.
"It's definitely not easy," said Williams. "It's always hard to play early in the season."
As well as the conditions, the tenacity of Giorgi made it difficult; the 28-year-old Italian always raises her level to play Williams, shown at Wimbledon two years ago, when she took the first set before losing in three.
She ran, she harried and she chased, and most importantly she always forced Williams to play another shot. At times that made the 38-year-old uncomfortable, especially off the backhand.
"She got a lot of balls back but that's okay," said Williams. "I have to be able to beat people that get balls back too."
The turning point in the first set came in the eighth game; Williams lasered some ground strokes, and landed a backhand within millimetres of the line to set up a break, which she converted to lead 5-3.
Williams was untroubled to close out the first set in 38 minutes, finished off by a vicious serve into the body.
In her 24th year on tour, Williams now cherishes the magic moments more.
"Usually when I hit a big shot I don't think about and now it's like 'oh that was nice'," said Williams. "I appreciate it more as opposed to even last year, I hit great shots and I just move on. It's nice to actually pat yourself on the back."
The second set was more clear cut. Williams broke Giorgi twice, as the Italian struggled on first serve, landing just 50 per cent.
