The 23-year-old Russian swept past Belgian Kirsten Flipkens 7-5, 6-1 to set up a meeting with 2006 champion Amelie Mauresmo, of France.
Safina, who has yet to win a Grand Slam title, made it into Wimbledon's second week for the first time. She has not conceded a set so far and is starting to emerge as a real threat to the grass-court specialists.
She will be a strong favourite to get past Mauresmo, who put out Flavia Pennetta, of Italy, 7-5, 6-3.
Mauresmo, the 17th seed, is launching a comeback bid after a couple of years in the doldrums.
And she said: "Compared to the last two years I have not even been talked about here in Wimbledon this week.
"Throughout the last few months it's been much better. I was enjoying myself a lot more.
"Hopefully, I'll have some more great moments on court. But mentally you just learn from playing matches.
Hewitt won his boys' singles first round match 6-4, 7-5 against Taipei's Liang-Chi Huang. But Hannah James lost 6-2, 6-2 to Russian Daria Gavrilova in the girls' singles first round.
She was joined through the exit door by Nicola George, who lost 6-4, 7-5 to Vivien Juhaszova.
Samantha Vickers went out at the same stage, beaten 6-1, 6-0 by Italy's Martina Trevisan.
Lewis Burton fared no better in the boys' singles, losing 4-6, 7-5, 4-6 to David Souto, of Venezuela. George Morgan was beaten 7-6, 6-2 by Bernard Tomic and Jack Carpenter was ousted 6-4, 7-5 by Sebastian Lavie. In mixed doubles, James Auckland and Elena Baltacha lost 6-1, 6-2 to Daniel Nestor and Elena Vesnina.
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