Rochus had to survive his third three-set match of the week to beat 2008 champion Kohlschreiber in 2 hours, 29 minutes.
He lost the first set in 71 minutes. But he played much more solidly in the second and third sets, chasing down every ball as Kohlschreiber became increasingly frustrated in the gusty conditions.
"All my matches this week have been so hard for me and it's fantastic to win this one," he said.
"At the end of the match I was really tired, but when you play in front of a crowd like this with an atmosphere like this, you give your best."