The visitors triumphed in a thrilling encounter at Edgeley Park on Friday night to move up to ninth in the table.
The Tigers have found life tough in the opening weeks of the season owing to a number of World Cup call-ups, but they dug deep when it mattered most.
Rookie wing Tom Brady's first-half try helped the Sharks into a 13-3 interval lead but second-half scores from Alesana Tuilagi, Martin Castrogiovanni, Toby Flood and Marcos Ayerza completed a stunning turnaround.
Sale named Wales flanker Andy Powell on the bench following his return from the World Cup last weekend as the hosts sought to maintain their fine start to the campaign.
Leicester hooker George Chuter made his 250th appearance for the club, replacing Tom Youngs in the front row, while Scott Hamilton came into midfield for the injured Manu Tuilagi.
It was Leicester who began quickest as a break from England flanker Tom Croft took him close before Sale fly-half Nick MacLeod missed a penalty from distance.
In the 11th minute, the Tigers led when England number 10 Flood slotted over a penalty but the response from the hosts was impressive.
Rob Miller went close down the left flank and then Brady saw a score ruled out on the opposite flank by the television match official.
Shortly before the half-hour mark, MacLeod kicked two penalties in quick succession to put his side 6-3 ahead and from there Sale began to take control.
They continued to probe and were rewarded three minutes before the break when Sale produced a fine counter-attack which led to them scoring a try through Brady.
A Leicester defender was penalised for not releasing the ball and a quick penalty tap led to Miller dashing forward to send Brady over in the left corner.
MacLeod added the extras to put the hosts 13-3 ahead at half-time before Flood missed a penalty shortly after the restart.
He then kicked one from in front of the posts to cut Sale's lead to seven points in the 50th minute, before Tuilagi collected a pass from Flood to take Leicester over the line in the 58th minute.
Flood added the extras, Castrogiovanni burrowed over in the right corner three minutes later and Flood then sauntered over in the 58th minute to put the Tigers in total control.
Argentina prop Ayerza grabbed Leicester's fourth with another close-range effort in the 70th minute to leave Sale stunned.
Flood, an influential presence throughout, converted all four tries in a 19-point haul to get Leicester's season up and running.
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