
Three-time champion Williams will face a Friday semi-final against the winner from teenagers Nicole Vaidisova and French Open finalist Ana Ivanovic.
Unseeded Williams found her way in gusty conditions in the first set against former US Open winner Kuznetsova, but was blown off course in the second.
The American went up a break, but lost it, only to re-break Kuznetsova to love for a 4-3 lead.
With that margin in hand, she still had trouble in closing out the win three games later as Kuznetsova saved four match points before finally drilling long to end the 56-minutes second set.
Williams, ranked 31st after a period of injury and inactivity, overcame 20 unforced errors as she stayed alive in her 11th Wimbledon appearance.
The pair are now level at 3-3 in their series.