Roux, from Durbanville, admitted nine counts of contravening the Electronic Communications and Transactions Act.
She illegally changed Burger's e-mail password then entered his office and sent e-mails using his computer, and later her cellphone.
Eskom said the court found that Roux, a specialised maintenance and support manager, abused her position, violated Burger's right to privacy and exposed Eskom's information to a security breach.
Senior power plant maintenance supervisor Millard, of Parklands, also pleaded guilty to contravening the Electronic Communications and Transactions Act.
"We are happy with the judgment as it shows how seriously we view the protection of the critical data that sits within Eskom," said Tebogo Rakau, Eskom's divisional executive for security.
"The fact that this breach did happen is also an eye-opener for us, highlighting the need to institute even tighter security measures to ensure the integrity of the Eskom database from internal and external threats."
Die Son reported in July that Burger consulted a lawyer when his affair with Roux ended. Her objective in hacking into his e-mail was to read correspondence between him and his lawyer, the newspaper said.
According to their LinkedIn profiles, Roux joined Eskom as a trainee in 2003 and Millard joined in 2007 as a supervisor.