The combat of Dessau (12 October 1813) saw an isolated division from Tauenzien's Corps defeated by French troops who were attempting to intercept Blücher and Bernadotte as they moved west down the Elbe.
A key moment in the Autumn Campaign of 1813 came in late September, when Napoleon decided to abandon the right bank of the Elbe at the same time as Blücher decided to march his Army of Silesia north-west down the river to join with Bernadotte's Army of the North. Blücher fought his way across the Elbe at Wartenberg (3 October 1813) and moved west.
Once Napoleon realised what was happening, he put his troops in motion heading north-west in an attempt to catch Blücher somewhere between Leipzig and the Elbe. This effort ended in failure, but he did manage to catch one division from the Army of the North.
Tauenzein's corps (Prussian) from the Army of the North had been left to form a link between Bernadotte and Blücher, but once Blücher reached the Elbe he was freed to move west towards the rest of the Army of the North. He took up a position at Dessau, on the River Mulde just to the south of the Elbe.
As part of Napoleon's attempts to catch Blücher and Bernadotte Reynier's corps moved to the north (right) bank of the Elbe, and advanced west along the river, lifiting the siege of Wittenberg as he went (pushing away Prussian forces under Thümen).
When Tauenzien learnt that Reynier was moving along the north bank of the river he realised that he was no longer safe at Dessau. He crossed to Rosslau, on the north bank of the Elbe, but chose to leave one division at Dessau.
This put it directly in Ney's path. His III Corps was advancing along the left bank of the Elbe, heading towards Dessau. On 12 October he attacked the isolated division at Dessau. The Prussians defended the town with some determination, but eventually they were defeated by General Delmas's 9th Division. The Prussians lost 2,000 men and four guns at Dessau.
They also lost the use of Tauentzien and Thümen, who retreated at some speed north towards Berlin. They were thus not present at the battle of Leipzig (16-19 October 1813).