Carson's transgression occurred in the 41st minute when he fumbled a seemingly harmless low shot from Gabby Agbonlahor, who had shot more in hope than conviction of scoring.
Earlier, Curtis Davies did his former club few favours as the central defender notched his first goal for Aston Villa to keep West Bromwich Albion firmly entrenched at the foot of the Premier League.
Poor Albion, who have collected only four points from their eleven away games, slumped to their eighth defeat away from The Hawthorns as Villa completed the double.
After his second-half performance, questions had to be asked why Albion did not start the game with Roman Bednar, who certainly livened up their attack in the second half.
Villa, last beaten at home by Albion in 1979, turned off the tap in the second half and maintained their record, although they allowed their near neighbours back into the game when James Morrison reduced the arrears five minutes into the second half.
As usual, Albion played some pleasing football with newcomer Jay Simpson from Arsenal showing up well in the early stages.
The vital turning point occurred in the 18th minute following a delightful three man move between Stiliyan Petrov, Gareth Barry and Ashley Young.
Unfortunately, no-one was on hand to convert Young's perfect cross from the left. Paul Robinson, however, decided to concede a corner.
Both Morrison and Jonathan Greening cleared efforts off the line before the ball went back to Barry on the right. His cross was headed home by Davies despite a packed Albion defence.
The goal turned on Villa, with Ashley Young in particular emerging as Albion's tormentor-in-chief as he demonstrated with several tricky runs. One such run nearly ended in a second goal, but Young's curling shot was just wide of the far post.
Albion's fate should have been sealed as early as the 31 minute when their defensive frailties were exposed. Robinson was caught hopelessly out of position as James Milner raced clear.
He provided a low cross for the on-rushing Steve Sidwell, but the former Arsenal and Chelsea player screwed his shot wide.
Four minutes before half-time Carson made his latest howler when he palmed in Agbonlahor's low, close-range shot after the England striker had collected a pass from Barry.
Albion, who had previously only scored three goals on their travels this season, hit back in the 50th minute when Morrison gave a good indication of why he has attracted the attention of Bolton.
The industrious Albion played latched onto a header down from substitute Bednar to crash his 15-yard shot past Brad Friedel, with the aid of a deflection.
In the following two minutes Carson distinguished himself with successive saves from Ashley Young and Sidwell to keep Albion in the game, but his earlier mistake ultimately proved to be the incident which decided the local derby.
Albion staged a determined late rally and Villa survived the onslaught and what appeared to be a strong penalty appeal in the last three minutes to complete the double.