Villa looked out of sorts during the opening 45 minutes and needed a fortuitous goal from Ashley Young to cancel out Steven Fletcher's opener.
But O'Neill's 'kick up the backside' worked wonders and Villa responded with four goals in 13 minutes from Downing (two), Emile Heskey and Gabriel Agbonlahor in running out 5-2 winners.
Sharpshooter: Stewart Downing (left) scores against Burnley
It kept Villa on course for a Champions League spot via a top-four finish in the Barclays Premier League as they put their recent goalscoring problems - just three in the previous seven league games - behind them.
Downing said: 'The manager wasn't very happy at half-time. It took a gee-up from him and a few other players to get us going because it wasn't acceptable really.
'It worked wonders because in the second half we looked a different team and played some great football.
'The manager is a great man motivator and half-time was the perfect example with a kick up the backside.
Confidence boost: Goal-scorer Downing (left) celebrates with Villa team-mate Gabriel Agbonlahor
'He demanded more of us as players and there are some big characters in the dressing room and a few things were said and it worked.
'It was a slow game for a long time and once we got the second goal, it gave us a bit of confidence and we played some great stuff in a 15-minute spell and killed the game off.'
Downing missed the first half of the season after his £12million move from Middlesbrough in the summer after breaking his foot in April, in a challenge with Villa skipper Stiliyan Petrov.
But he has quickly made a big impression with O'Neill. He said: 'I think Stewart has done wonderfully well for us. He's had no pre-season, he came straight into the side from injury and has been excellent.
'He did some wonderful things in the game against Burnley. I think he is just getting really properly fit. Sometimes the crowd get a bit anxious when he goes 10 yards and then checks back.
'But the first goal he stuck in brilliantly and you can immediately see a lift of confidence - and his second goal came because the confidence was up.'
Burnley remain in the bottom three after their second-half collapse left them with only one point on their travels this season.
Big impression: Downing slides in his first goal against Burnley
Manager Brian Laws admitted: 'We did not regroup well after their equaliser and the second goal was a killer. It was very sloppy.
'That led to a crazy 12-13 minutes that lost us the game and you can't rectify anything after that.
'But we will get a result away from home this season. We will break this barrier.'
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