The former England left-back struck from the edge of the box as his left-footed effort sailed past Brad Guzan as Nigel Pearson's men took a much-needed three points
The 33-year old was on hand to drive home a half-volley on the stroke of half-time to end a wait of over five years since his last top-flight strike and make it three league games unbeaten for the hosts.
Leicester enjoyed the better of the first-half exchanges with David Nugent at the centre of their best chances, the striker hitting the crossbar just before the opening goal.
Matty James saw red late on for a dangerous challenge on Jores Okore, an incident that also saw Villa's Ciaran Clark shown a second yellow for confronting the 23-year old.
Villa again struggled in front of goal, drawing a blank for the 12th time this season to leave Paul Lambert's side in danger of being dragged into a relegation battle.
Meanwhile, Leicester - who remain bottom - have not tasted defeat in four games in all competitions, their best run of form so far this season.
The recent upturn in results saw Leicester boss Nigel Pearson talk up the levels of confidence among his players before this contest, and they began on the front foot against an Aston Villa side that had previously found the net just once in their last five Premier League games.
Nugent volleyed wide from Danny Simpson's diagonal cross after six minutes and poked another effort off target following a darting breakaway run from former Villa man Marc Albrighton down the left seven minutes later.
But there were still signs of defensive frailty from the hosts, who made four alterations from the win over Newcastle United last week, as Gabriel Agbonlahor burst through the middle before sending a 25-yard effort high and wide, snubbing better options.
Nugent came close yet again after crashing a half-volley onto the crossbar four minutes before half-time, but Konchesky finally broke the deadlock deep into first-half stoppage time.
Villa failed to deal with Leonardo Ulloa's cross, with a clearance only coming as far as the waiting Konchesky, who drilled home a low drive from the edge of the area.
Ex-Villa winger Albrighton had only made one previous Premier League start for the hosts, but proved to be a thorn in the side of his former employers all afternoon.
He was nearly at the heart of a second goal, whipping in a fantastic cross for an unmarked James, whose powered header was superbly tipped over by Guzan.
And Albrighton got a chance to test the American himself on the hour, shaking off his man inside the area to force a smart save.
Alan Hutton came close to an unlikely equaliser but failed to keep his angled shot under the bar 20 minutes before the end, before Tom Cleverley inexplicably fired over from close range after the hosts failed to clear Joe Cole's corner.
Andreas Weimann and Kieran Richardson were introduced as Villa looked to salvage a point in the last 15 minutes, but they failed to make the difference.
Aly Cissokho should have levelled matters in the final 10 minutes, but blazed his shot overe before red-card drama dominated the closing stages.
Both teams were reduced to 10 men after James was dismissed for a lunging challenge on Okore, while Clark was shown a second yellow for squaring up to the midfielder on another bad afternoon for Lambert's men.