Frederic Piquionne was the star as Portsmouth put their poor league form to one side to easily qualify for the quarter-finals of the Carling Cup.
The much-changed hosts were always in control after Piquionne headed past Steve Simonsen on 17 minutes.
The on-loan Lyon striker then turned provider for Danny Webber to cut in and drive home, before stabbing in his side's third after a Simonsen mistake.
Kanu added a fourth from close range late on to cap a dominant display.
The Carling Cup has provided some welcome relief from a horrendous start to the Premier League season for Portsmouth, and Paul Hart's side can now look forward to a place in the quarter-finals.
Tony Pulis had illustrated the Carling Cup's order in his priority list this season by making 10 changes to the side that beat Spurs at the weekend, but Stoke were still surprising lacklustre throughout.
Piquionne was one of seven changes for Pompey, but he certainly made a strong case for a starting place against Wigan on Saturday.
The French striker opened the scoring by outjumping Danny Higginbotham after a fine cross from Nadir Belhadj.
Portsmouth never looked in danger after that point, but had to wait until the 56th minute for Webber to make the game safe with a fine finish from the inside-left channel.
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