Reduction of N,N-dimethylbenzamide with LiAlH4
Here's the mechanism. The key is the second step, it's the lone pair of nitrogen that attacks the carbon, and not the lone pair of oxygen.

The reasoning is that the lone pair of nitrogen is more reactive because of the two electron-donating methyl groups attached to the nitrogen atom. The electron density is higher on the nitrogen atom than the oxygen atom.

The second reason is that the oxygen anion as a leaving group is much more stable than the nitrogen anion R2N- you would have gotten if the reaction led to your product.