'Good banter': Smith and Archer clash in Gabba Ashes Test
The hosts won the day-night Test by an emphatic eight wickets in Brisbane to seize a 2-0 lead in the series.
Smith hit the winning runs including pulling Gus Atkinson for a huge six over square leg to finish the job in style.
His verbal joust with express paceman Archer shortly before that made for captivating viewing as they went head-to-head.
"Bowl fast when there's nothing going on, champion," stump mics captured Smith telling Archer.
Smith laughed off the exchange afterwards.
"It stays on the field," the ABC quoted Smith as saying.
"It was good, good banter. He's a good competitor and he comes hard at you, so it was good fun."
The series now heads to Adelaide with Australia having one hand on the Ashes urn.
Despite another one-sided victory to go with the opening Test in Perth, Smith remains wary of Ben Stokes's wounded men.
"They're obviously a really good side and they've played great cricket for a couple of years now," he said.
"They're going to come back hard -- whether they come back and play really aggressive or take the foot off the pedal a little bit and try and prolong the game a bit, we'll wait and see.
"But you know, they've got some really good players in their team and they're going to come back hard at us next game."
Smith also played a crucial role in the field including a spectacular diving effort to dismiss Will Jacks in the second innings.
With wicketkeeper Alex Carey standing up to the stumps, Jacks got an inside edge to seamer Michael Neser and Smith dived full length to his left to take the one-handed catch.
"I was pretty happy with that one -- low to my left, pink ball, under lights, the situation of the game and a huge partnership to break," he said.
"So yeah, I was pretty excited."
Smith said Australia could not have asked for a better start.
"It's been a wonderful couple of weeks for the team," he said.
"I think we've played some sensational cricket. We've identified moments in the game and made the most of them."