Both sides seemed overwhelmed by the importance of a match which lacked quality and chances.
The paltry total of two shots on target was the joint fewest of any Premier League game this season.
Villa recovered from a poor first half showing in which they went behind to a Steven Fletcher effort to restore parity by the interval through Ashley Young.
But four quick goals after the break including a Downing brace, Emile Heskey and Gabriel Agbonlahor changed the picture before Martin Patterson's injury-time consolation.
Villa boss Martin O'Neill: "We needed to threaten them a lot more than we had done in the first half and close players down, and we did that successfully.
"We had started a bit slowly but that burst after half-time was conclusive and will boost our confidence.
"The equaliser galvanised us and the spurt after half-time was exceptional."
Burnley boss Brian Laws: "It was a 13-minute chunk where we fell apart, that is the disappointing thing.
"We limited Villa to very little in the first half - they had only pockets of chances - but the second goal was the main turning point.
"After that, instead of shutting up shop, we opened up - and, if you do that, the good sides will hurt you."
Blackburn added to the woes of local rivals Bolton with a deserved 3-0 win.
Goals from Nikola Kalinic, Jason Roberts and Gael Givet saw Rovers to what was a comfortable win in snowy conditions at Ewood Park.
The victory eased Blackburn further clear of but Bolton remain in the drop zone after a fifth league game in a row without scoring.
Tottenham's second league win of the year, 3-0 at Wigan, was enough keep them in the Champions League places.
Jermain Defoe, who scored five goals against Wigan earlier in the campaign, made the breakthrough in the 27th minute from what appeared to be an offside position.
Late goals from Roman Pavlyuchenko added lustre to the scoreline as Spurs eased to three points.
The Latics remain just two points off the drop zone as a result of the defeat and on this showing look destined for the Championship next season.
Fulham came from behind to claim all three points courtesy of Bobby Zamora's late free kick winner in front of England coach Fabio Capello.
Zamora's strike made it 15 goals in 32 starts, provoking chants of 'Bobby for England' from the Cottagers faithful.
An own goal from Chris Baird had given Birmingham the lead before Damien Duff fired a spectacular equaliser.