The win set up a tie against arch rivals Millwall.
In the North American derby, the United States defeated Mexico 2-0 to set up a quarter-final tie with Germany.
Baltacha battled tough conditions to overcome the 21-year-old wild card and set up a second-round tie with fourth seed Flavia Pennetta.
North Carolina State (3-8, 2-6) didn't go without a fight, scoring twice in the final 2 minutes 36 seconds to set up a possible tie with seven seconds left.
The result set up a semi-final tie with Partizan, a tie that would take United back to for the first time since the tragedy in Munich.
A 6-2 aggregate victory set up a tie against Auxerre of France in the second round who they beat 3-2 on aggregate.
This loss however set up a memorable tie versus the United States with the winner to remain in the World Group for the following year.
This set up a tie in the first round against Dinamo Tirana from Albania.
It sets up a fourth-round tie against Chelsea after Danny Gabbidon scored with a second-half header.