Josh Adams had appeared to spare the blushes of the lacklustre when he crossed 11 minutes from time to put Wales ahead.
Kieran Crowley's Italy looked set for a 37th successive defeat in the competition at that stage, but there was to be one final twist in Cardiff.
Ange Capuozzo burst away from the tiring Wales defence and offloaded to Padovani, who went in under the posts before Paolo Garbisi converted to complete a remarkable victory.
