After losing to Rochdale and MK Dons, Paul Warne's side faced a Cobblers team fighting to avoid relegation.
But it was the Millers who opened the scoring, Smith firing home on 17 minutes.
David Ball doubled their advantage just after the hour mark, before Richie Towell made it 3-0.
“I’m very pleased,” said Millers boss Paul Warne. “I thought our performance was very good.
“After a couple of defeats, we needed to put a flag back into the ground and we performed very well today. We limited them to very few chances and then got three good goals ourselves, which was hugely pleasing.
“It’s nice that both my strikers scored.
“I thought Smudge was virtually unplayable today. I thought he was excellent.
“I thought Will Vaulks, who played centre-half was very good while Matty (Palmer), who played his first game for a while, showed how he can control a game, in the second-half of the game.”