Stiliyan Petrov’s early own goal was cancelled out by Emile Heskey’s equaliser, with James Milner establishing a lead for the visitors before Downing struck late on.
Kanu pulled one back to set up an exciting finale but Ashley Young made sure of Villa’s victory.
It means Avram Grant can now concentrate on his club’s survival campaign in the Barclays Premier League.
Grant has been labelled an unlucky manager after John Terry’s slip denied him the Champions League title – but after 10 minutes his Pompey side were ahead with a fortuitous opener.
Danny Webber’s corner was poorly executed and should not have cleared Petrov at the near post, but the Villa skipper sliced into his own goal despite Milner being positioned on the line.
The lead only lasted two minutes though with Milner placing the ball beyond the Pompey defence and Heskey chipping over Portsmouth goalkeeper Asmir Begovic and in.
The visitors were ahead in the 27th minute through a classic strike from Milner. The England international cut inside from the left flank after collecting winger Young’s throw-in and he gave Begovic no chance with his drive into the far corner.
Downing’s moment came 16 minutes from full-time. Winger Young sent over a cross from the right that took a wicked deflection and span across Begovic’s goal – and Downing judged the bounce perfectly to head home.
Kanu bundled in a scrappy goal from close range, but Young immediately tucked away Agbonlahor’s cross to restore the two-goal cushion.
PORTSMOUTH: Begovic, Vanden Borre, Kaboul, Ben-Haim, Hreidarsson, Yebda, Brown, Hughes (Wilson 85), Belhadj, Webber (Kanu 65), Utaka (Piquionne 76).
ASTON VILLA: Guzan, Luke Young, Dunne, Cuellar, Warnock, Milner, Petrov, Downing, Agbonlahor, Heskey (Delfouneso 90), Ashley Young. Referee: Lee Mason (Lancashire).