The Germany playmaker scored two early goals before setting up a third to help the German champions seal their 11th Cup triumph. They also won the double in 1969, 1986 and 2000.
Bayern comfortably won their 18th league title with four games remaining in the season.
Ballack headed Bayern into the lead from a free kick by England midfielder Owen Hargreaves on three minutes and doubled the advantage from a penalty seven minutes later after Hargreaves was brought down in the box.
He then set up Peru striker Claudio Pizarro, who flicked the ball over Kaiserslautern goalkeeper Tim Wiese to put Bayern 3-0 up five minutes into the second half.
"Last year I lost the final but this time I've got the trophy," said Ballack. "It was important for all the team to win today. The early goals were the foundation stones for our victory."
Kaiserslautern, who battled against relegation and financial collapse this season, had midfielder Marian Hristov sent off for a dangerous tackle on Bayern's Elber in the 78th minute.
Germany striker Miroslav Klose pulled one back for Kaiserslautern with a header two minutes later, but the game was already beyond doubt.
The four-times German champions were playing their seventh Cup final and were hoping to lifting the trophy for the third time after 1990 and 1996 but a determined Bayern side ruined their plans.
"I hadn't expected the game to be like that," said Kaiserslautern coach Erik Gerets. "It was all over before it really started.
"At halftime I noticed that the guys were resigned. I had the feeling very early that we were not going to make it."
With Bayern going into the Champions League, the southwesterners knew they would enter the UEFA Cup even if they lost the final.
They came close to reducing the arrears just after Ballack's penalty, when Portugal midfielder Jose Manuel Dominguez headed narrowly wide from a cross by Harry Koch.
But Bayern were in control for most of the game and failed to open a 4-0 lead when a low volley from just inside the box by Pizarro flirted with the post in the 54th minute.
Tight defending and a commanding midfield display helped Bayern add to their rich collection of silverware as they signed off in style after a season marred by their embarrassing first-stage exit from the Champions League.