The Brits started ferociously on Wimbledon's Court 1 and romped to a 6-1 win in the opening set in just 27 minutes.
They found a decisive break early in the second, but the Germans broke back to level at 2-2.
However, Robson and Murray broke again instantly to put themselves back in control.
The Germans continued to battle and were rewarded with another break to make it 4-4.
Both teams then held serve over the next four games as the match went into a tie-break.
The British duo raced into a 3-0 lead, but Lisicki and Kas won the next six points to put them on the verge of levelling the match.
Robson and Murray then broke back to get themselves back on terms but the Germans again hung in there to take it 9-7.
Into the Champions tie-break and the Brits held their nerve to see out the match 10-7 in front of an ecstatic home crowd.