It was Sale who dominated the first half despite holding just an 8-6 lead through Rob Miller's unconverted try and a Nick Macleod penalty.
Leicester's George Ford, deputising for Toby Flood, responded with two three-pointers in what was initially a disappointing team display.
But they were revitalised in the second period and scored 14 unanswered points through the boot of Ford and a try from Youngs on his return from injury.
Sale's mercurial fly-half Danny Cipriani had to pull out from the substitutes' bench late on due to flu but the player who has been preferred to him in recent weeks, Macleod, started the match impressively by controlling proceedings and allowing the hosts to get on top early in the encounter.
They deservedly went ahead through a well-worked try. Number eight Andy Powell had already threatened before Will Addison took advantage of disorganisation in the visitors' defensive line with a quick throw-in.
It was collected by Mark Cueto who took the ball into contact before it was shipped out to Miller, who scampered over in the corner.
Despite being dominated for the opening 10 minutes, the Tigers eventually ground their way into the match and Ford rewarded their brief period of possession with a penalty.
However, Macleod responded for the Manchester outfit with a three-pointer of his own four minutes later to give them an 8-3 lead.
Ford once again reduced the arrears to two points but it was an impressive first half from Bryan Redpath's much-maligned charges.
The pressure certainly got to Leicester's Vereniki Goneva, who deliberately knocked on Cillian Willis' attempted pass to Addison and was subsequently sin-binned.
But the hosts have struggled to take the chances that have presented themselves throughout this season, as well as showing an inability to control the forward battle for long enough periods.
That issue once again came back to haunt the Sharks when Addison was unable to touch down after they were camped on the Tigers' line.
Although the visitors produced the odd burst through the ever-dangerous centre duo of Anthony Allen and Manu Tuilagi, it was Sale who deservedly had the advantage at the break.
However, the midlands outfit came out with far more intent in the second period and went ahead through the fly-half's third from the tee.
Leicester then stretched their lead when Youngs went over and Ford kicked his fourth penalty.
It was perhaps harsh on the hosts, but it was typically clinical by last year's beaten finalists.
The Sharks continued to battle away, though, and threatened through breaks from Miller and substitute half-back Nathan Fowles.
But it was not to be as Ford sealed the victory with a three-pointer after Joe Ward had been yellow-carded for Sale.
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