England rode on a fine debut ton from Rory Burns to gain a crucial 90-run lead.
Australia looked in trouble after quick wickets, but Smith (142) and Matthew Wade (110) helped them to post 487/7.
England were dismantled in their chase.
Smith scripts a host of Ashes records
Smith, with two tons, has amassed overall 1,116 runs in his past 10 Ashes innings.
The senior cricketer also became the fifth Australian batsman to score hundreds in both innings of an Ashes Test.
He joined the likes of Warren Bardsley (1909), Arthur Morris (1946/47), Steve Waugh (1997) and Matthew Hayden (2002/03).
Smith now has 10 career Ashes centuries in total.
Smith equals Kohli and Inzamam with this feat
Smith now has 25 career Test centuries.
He equalled Indian cricket team skipper Virat Kohli and former Pakistan great Inzamam-ul-Haq (both 25 Test tons).
He has the seventh most hundreds for Australia in Tests.
Smith is only behind Sir Donald Bradman (19) in terms of Ashes tons by an Aussie.
He needs three more tons to surpass former England legend Sir Jack Hobbs (12).
Smith second fastest to 25 Test hundreds
Steve Smith now becomes the 22nd batsman to make 25 or more Test 100s. Fewest innings to reach 25th Test 100 68 - Don Bradman🇦🇺 119 - Steve Smith 🇦🇺 127 - Virat Kohli 🇮🇳 130 - Sachin Tendulkar 🇮🇳 138 - Sunil Gavaskar 🇮🇳 139 - Matthew Hayden 🇦🇺#Ashes#Ashes19#EngvAus#EngvsAus