Ballack redirected Lampard's free-kick cross with a glancing header to the near post.
Lampard scored with a tap-in after Michael Essien beat two defenders and passed a low ball into the goal area.
"I feel good because our target was to be in the semifinal," said Chelsea coach Avram Grant. "It was not easy. We started well but then it was a nervous game ... the most important thing was the result."
"The players did their utmost but we were not lucky," Fenerbahce coach Zico said. "We created chances but could not turn them into goals," the former Brazil international said.
"When you concede in the first five minutes with a free header from an unnecessary foul ... of course you have to chase the game from then on.
"But it has been a great experience, playing great teams and our motivation is to get better ... and to contest the Champions League again next season.