Paul Lambert's men fell behind to Leonardo Ulloa's opener at Villa Park on Sunday, but Ciaran Clark's first Premier League goal since September 2012 quickly levelled proceedings.
The turnaround was completed by another unlikely scorer in the form of Hutton, who had not scored since playing for Tottenham in November 2010, before the visitors had Paul Konchesky sent off with 10 minutes remaining.
Leicester struck the first blow when Ulloa capitalised on a rare error from Villa goalkeeper Brad Guzan for his first goal since September.
Clark took advantage of some slack Leicester defending to level the match before the break, though, and full-back Hutton - undergoing somewhat of a renaissance this season after seemingly being shut out at Villa Park - kept his cool with the winner in 71st minute.
Villa have now won back to back matches in the top flight and climb to 11th as a result of their first home victory since August, while Leicester have now failed to win in 10 matches and are bottom of the table.
The home side started on the front foot, but it was the visitors who opened the scoring in the 13th minute.
Riyad Mahrez jinked his way in from the right flank and his tame shot, which took a slight deflection off Clark, should have been held by Guzan but the goalkeeper spilled the ball into the path of Ulloa, who tapped home the rebound to end a nine-match goal drought.
The lead lasted just four minutes, though, as the unmarked Clark stooped low to head Ashley Westwood's free-kick past Kasper Schmeichel for his first Villa goal since September 2012.
The hosts were dealt a blow before half-time when Westwood was carried off after a poorly timed challenge from Jamie Vardy - who received a yellow card.
Leicester also made a change at the break with Ulloa coming off for David Nugent after failing to shake off an injury sustained in a strong challenge from Clark.
Villa created the better chances after the restart and Schmeichel did well to race off his line and force Benteke's shot to loop wide after the Belgium international held his run to latch onto Keiran Richardson's throughball.
Nugent almost put Leicester ahead against the run of play in the 68th minute with a volley bound for the top-left corner of the net until Guzan did superbly to deny him with a fine save.
Villa deservedly moved ahead with just under 20 minutes remaining, though, when Benteke's excellent cross-field pass picked out Hutton's marauding run into the area and he calmly slotted past Schmeichel at the near post.
Benteke was then twice denied by excellent point-blank stops from Schmeichel as Villa turned the screw, before Leicester's task was made even more difficult when Konchesky saw red for a challenge on Hutton which resulted in the pair squaring up 11 minutes from time.
Hutton was cautioned for his reaction and Villa had to hold firm to withstand some late pressure, substitute Chris Wood coming closest with a stinging half-volley from the edge of the box that went wide as Nigel Pearson's side were beaten again.
