Australian captain Tim Paine hailed Steve Smith's efforts with the willow after the visitors romped home to a 251-run win over England in the first Ashes Test at Edgbaston.

Smith scored 144 and 142 in the match and thus became the first Australian to score two centuries in an Ashes Test since Matthew Hayden in 2002. His tons were instrumental in Australia wrestling control especially in the first innings in which they went from 122/8 to 284 with Smith being the last man to be dismissed.

"Running out of things to say about him, probably the best Test match performance we've seen," said Paine in the post-match presentation ceremony.

He also praised Matthew Wade, who scored his first Test century since 2013 in the second innings which helped consolidate Australia's position of strength on Day 4.

"Wadey I've seen up close at Tasmania for the last couple of years, he's in form and a really good place," said Paine.

Australia needed to take 10 wickets on the final day to win the match. Nathan Lyon took six and Pat Cummins took four to help them take a 1-0 lead in the series.

"Always hard to come to a Test match on day five, with the pressure on your shoulders. But we put pressure on the other end as well, Nathan took the spoils but we shared it around. This morning, our bowling was sensational," he said.

Paine also commended his team for the way they handled the crowd. "Didn't matter where it was, we know the crowd's going to be against us. The guys handled themselves well, and stuck to their guns," he said.

Smith and David Warner, who were playing their first Test since serving bans for their involvement in the 2018 Newlands ball tampering scandal, were the subject of boos throughout. While Smith turned it around somewhat with his twin tons, Warner was jot as prolific with the bat but an image of him holding out his pockets to the crowd to show that he has no sandpaper in his hands was well received.