Downing suffered a fractured foot in May, but Villa boss Martin O’Neill deemed him ready for a starting place and he wrapped up victory at Fratton Park.
Avram Grant’s side had taken the lead after just 10 minutes when Stiliyan Petrov sliced a corner into his own net.
However, the visitors replied just two minutes later through Emile Heskey.
England winger James Milner then struck just before the half-hour mark to nudge O’Neill’s men ahead.
Downing increased the visitors’ advantage with a well-taken header on 74 minutes.
Kanu poked home to give Pompey a lifeline on 87 minutes but Villa hit back again within two minutes, Ashley Young firing home to put them into the last four.