The Sharks have not won a game since March, but a sharp performance forced the Tigers into a series of uncharacteristic errors that were punished by the boot of an inspired Braam van Straaten.
Graeme Bond opened the scoring after only four minutes with a beautifully taken try that stemmed from turnover ball.
The former Wallaby centre received an inside pass from wing Steve Hanley and set-off from the half-way line before coming off his left foot to beat a poor challenge from former England fullback Tim Stimpson.
Van Straaten added the well-taken conversion from out wide before Stimpson made amends with a central 45-metre penalty.
A scrappy error-strewn period followed and as rain began to fall, Van Straaten added two more penalties as the Tigers struggled to assert themselves.
The former Springbok inside back made better use of the boot than Stimpson, who missed two easy chance before half-time.
The Tigers failed to find their claws in the changing-room and skipper Josh Kronfeld immediately gave away a needless penalty under the post early in the second half and Van Sraaten stepped up to help himself to three more points.
Some sustained Leciester pressure and a Stimpson penalty followed, but the Shark defence held strong and a deliberate knock-on by a visibly frustrated Kronfeld led to his sin-binning and another successful Van Straaten penalty.
More Leicester pressure resulted in a try from replacement Sam Vesty, who nipped through Sale's midfield with a show-and-go to score under the posts. Stimpson added the easy conversion.
In a desperate finish, Sale responded with another penalty before Stimpson managed to find the sticks to win his team a bonus point, which, at this early stage of the season, could just help his side in the final outcome in 2004.
For Leicester:Try: VestyCon: StimpsonPens: Stimpson 3
For Sale:Try: BondCon: Van StraatenPens: Van Straaten 5