Sharks became the first club since play-offs were introduced three seasons ago to secure silverware after finishing top following a 22-game regular season.
First-half tries from wings Mark Cueto and Oriol Ripol, plus flanker Magnus Lund's touchdown - all three scores were referred to the video referee - left Leicester licking their wounds.
Tigers' England flanker Lewis Moody claimed an opportunist score and substitute James Hamilton powered over six minutes from time, but the Sharks eased home through a 23-point contribution from fly-half Charlie Hodgson and substitute Chris Mayor's injury-time breakaway.
England ace Hodgson booted six penalties, a drop-goal and conversion, giving once unfashionable Sale Premiership title glory and extending Leicester's barren run of four seasons without a major trophy.
Hodgson landed an early penalty and things quickly deteriorated for Leicester when Sale stung them through an opportunist try.
Hodgson's well-placed cross-kick drifted over the head of Leicester full-back Geordan Murphy, and Cueto reacted to a kind ricochet by touching down in the corner.
It was a dream start for Sale, yet Leicester slashed their arrears within two minutes of Cueto's strike.
Hodgson saw an attempted defensive clearance charged down by Tigers flanker Shane Jennings and, before Sale could respond, Tigers centre Ollie Smith hacked on before Moody - after confirmation from video official Geoff Warren - touched down.
Andy Goode's effortless touchline conversion brought Leicester back to 8-7, yet Sale displayed true title credentials by striking another blow as a breathless opening quarter reached its conclusion.
Undeterred by Moody's try, Sale launched a menacing break through Wigglesworth and, when Goode fumbled badly in defence, Lund reacted superbly to kick clear and win the touchdown race, which was confirmed when referee Dave Pearson - for a third time in succession - sought video replay clarification.
Hodgson pushed his conversion attempt narrowly wide, but Sale continued to establish threatening field position on a slippery surface, and were good value for their six-point advantage.
Hodgson landed his second successful penalty 10 minutes before the break, only for Goode to find his range from 45 metres and keep an intriguing final firmly in the melting pot.
Sale looked far more dangerous with ball in hand, yet Leicester's naturally attritional approach meant the Sharks could hardly relax until a moment of Hodgson magic left Tigers' defence at sixes and sevens.
The timing of the England star's break bewildered Leicester and, as a huge gap opened up in front of him, he sent Ripol scampering over for an outstanding try.
Hodgson converted for good measure, sending Sale in at half-time 23-10 ahead and on course to be crowned English champions.
Sale were in no mood to relax, and two further Hodgson penalties after a Goode three-pointer hoisted them 29-13 ahead before another Hodgson penalty, a short-range drop-goal and Mayor's last-gasp effort, converted by replacement Valentin Courrent, condemned Leicester to a miserably fruitless afternoon.