Finding shortest paths in a DAG is simpler than Dijkstra. No need for a priority queue or visited set. Process nodes in topological order. For each node u, relax all outgoing edges (u,v) by trying to update dp[v] = min(dp[v], dp[u] + w(u,v)).
When you reach node v, all possible paths to v have been considered. This runs in O(V+E), faster than Dijkstra's O((V+E)logV). The topological order guarantees you process nodes in the right sequence.
Space complexity is O(V) for the data structures used.