Longest path in a DAG: source to sink?
First, notice that your topological sort comment isn't quite right, because other nodes can be sinks than the last node in a topological sort.

To your original question: Consider some path in a DAG that is not from a source to a sink. Can you show that this path can be made longer? (This implies that the longest path must be from a source to a sink.)

For example, if the path does not start at a source, then it has at least one incoming edge... (make sure you use the fact that the graph is a DAG).