Burnley were given an early boost when Steve Fletcher opened the scoring but this was cancelled out before half-time by Ashley Young.
Downing then transformed the game with his brace of goals to be followed by efforts from Emile Heskey and Gabby Agbonlahor as Burnley slumped to their eighth successive away defeat.
With the worst away record in the English league Burnley opened brightly by taking a shock tenth minute lead - their first away goal in 9hrs 10mins of play. But was a false dawn as subsequent events highlighted.
Villa had appeared to be the more dangerous at the start and Burnley could have been in serious trouble if Stiliyan Petrov had been more accurate with his shooting after he had been set up by Agbonlahor.
Burnley's response in their next attack was to go ahead with a surprise goal. Jack Cork, making his first start since his latest move from Chelsea, set up the goal for striker Steve Fletcher, who was on hand to tap home a cross from David Nugent for his eleventh goal of the season.
Nugent very nearly added to Burnley's lead when his shot took a wicked deflection and bounced just wide of the post.
On-loan defender Leon Cort from Stoke was more than holding his own against England strikers Agbonlahor and Emile Heskey.
Heskey did manage to escape the attention of Cort in the 24th minute but his deflected header from Downing's cross was poorly directed and Burnley had another escape.
But in the 32nd minute Villa were back on level terms. A short corner by Young to James Milner and a return pass resulted in a shot by Young which went through the legs of Tyrone Mears and into the net.
The game went off the boil for a spell and at the start of the second period it was Burnley who were well on top, but the match was changed in a dramatic five-minute spell when Villa notched three goals.
A superb move originated by Heskey with a pass to Agbonlaho,r who lobbed a pass into the path of Young who squared the ball to the onrushing Downing to hammer home a low shot into the far corner of the net for his first league goal for Villa.
After waiting so long for this goal, Downing proved it was no fluke two minutes with his second when he picked up a Milner pass, turned and shot with his left foot past a helpless Brian Jensen.
An inspired Downing was on fire and he attempted to grab his hat-trick only to see his effort blocked by the Burnley defensive wall.
But there was no respite for Burnley, as Villa added a fourth goal when Heskey glided home a left-wing cross from Agbonlahor in the 61st minute.
Shell-shocked Burnley were in total disarray and the 69th minute Milner carved open the visitors' defence for Agbonlahor to notch Villa's fifth despite the attention of Clarke Carlisle.
Martin Paterson notched an 88th consolation goal for struggling Burnley.