The Blues were struggling to conjure up a winner at Stamford Bridge after Ballack's first-half header had been cancelled out by Wayne Rooney.
With regular penalty taker Frank Lampard absent following the death of his mother, Ballack took on the responsibility to score from 12 yards.
"It's always in big games in the end you have to score and, for me, it's no problem," Ballack told Sky Sports 1.
"I can handle the pressure. It's always a good situation if you're under pressure. I like this."
Ballack also dedicated the victory, which moved Chelsea level on points with United at the top of the table, to the absent Lampard.
He added: "I have to say the victory is for Frank and his family. We don't forget.
"It's a difficult time for everybody, especially for his family. It was a day for him today."
"After the game it is fine," continued Ballack. "It can happen during the game.
"Everybody wants to win, he, me and everybody. It's a great victory for the team, so it's not important."