Turkish striker Sanli Tuncay gave the Teesiders victory as he capitalised on two defensive clangers from Nicky Shorey and Sidwell.
The Villa midfielder had restored parity rapidly after Tuncay's opener but his short backpass two minutes from time cost Martin O'Neill's men a point.
Sidwell was making his first start in the Premier League for the Claret and Blue and had looked assured during the first 45 minutes.
But, to use the old cliché 'It was a game of two halves' for the Chelsea man as he faded after the break and proceeded to gift Boro the winner.
O'Neill had left John Carew out of the 18 and opted to play Gabby Agbonlahor in a lone role up front.
And without the Norwegian targetman, Villa struggled to create clear cut chances as James Milner and Ashley Young toiled on the wings.
Boro played tight, concise football, which caused problems throughout the first half and it was no surprise when they opened the scoring on 34 minutes.
With Gareth Southgate in the opposition dugout, there was a touch of irony about Villa's horror show in defence which let Boro in.
Southgate, such a composed defender for Villa, would have been embarrassed had he made a mistake like Shorey did during his playing days.
The former Reading left back completely failed to connect with the ball and it fell to Tuncay on the edge of the six yard box to slot in.
Sidwell then levelled matters after the ball ricocheted around the Boro area and fell to James Milner, who hung up a fine back post cross.
The ginger dynamo was able to rise above his man and head home past despairing keeper Ross Turnbull.
The away side weren't perturbed by the goal, though, and continued to play in a fluent fashion.
But after the break Villa went close as Agbonlahor dashed past Chris Riggott and tested Turnbull when one on one.
Milner was next to test the Boro stopper as he sent his shot against the keeper's legs after a good pull back from Gareth Barry.
The flying winger really should have scored to finish off a fine move from the home side.
And Villa were made to pay for their profligacy as Boro pushed forward.
Firstly, Riggott had a header cleared off the line by Young and then Afonso Alves embarrassingly missed from three yards after Brad Friedel parried into his path.
Villa thought they had escaped unscathed and continued to go for the victory with Marlon Harewood brought on to strengthen the attack.
But with minutes remaining, Sidwell crushed any hopes of a win for Villa with a weak back pass that fell to Tuncay who rifled home.
The stadium fell silent as Friedel pressed his cheek against the turf in dismay.
Sidwell collapsed in a heap, seemingly stunned by what he had done and looked like he wanted the ground to swallow him up.
Villa Park briefly had an element of the Bernabeu, a touch of the Nou Camp, as the small pocket of Boro fans started a victory chorus, high up in the Doug Ellis stand.
The weather didn't exactly match that you would expect at those venues as the rain continued to pour down as the final whistle blew.
The tide of water which engulfed the stadium washed away Villa's unbeaten record and took with it the confidence from the start of the season.
Fans may now be wondering where the next win is coming from with Arsenal and Manchester United the next two fixtures.
But, as they will know Villa are particularly unpredictable and could just claim a shock win at the Emirates next Saturday.