Success for Tigers sees them move into fourth place in the Aviva Premiership after beating their opponents by three tries to two, although a vital bonus point proved beyond them.
Richard Cockerill's side appeared to be running away with it after racing into a 17-0 lead thanks to a penalty try and Geordan Murphy's score, but Fraser McKenzie crossed for Sharks to keep them in the game.
Alesana Tuilagi restored Tigers' lead and although Rob Miller kept the visitors' hopes alive Leicester just held the edge in an entertaining match.
Sale got 2012 off to the worst possible start when flanker David Seymour and prop Henry Thomas - promoted from the bench with Tony Buckley absent ill - were involved in a sickening clash of heads in the second minute.
Thomas dashed off to get a gash above the eye seen to, and when he returned he failed to see out the half after picking up what looked like a serious knee injury. Seymour was in no shape to continue though and is likely to be out for at least a fortnight with a clear case of concussion.
It meant the Sharks were on the back foot from the restart, Tigers camped out in the opposition 22 before the referee awarded a penalty try following a succession of failed scrums.
Sharks tried to work their way back into the game with a good spell of possession, but it produced little and when they went over the top Toby Flood had the chance to extend the lead.
The penalty was pulled to the left, but Tigers were immediately on the attack and when Flood put Twelvetrees through a hole the returning Murphy was on hand to finish off next to the posts - Flood this time making no mistake.
At 14-0 inside 20 minutes it looked a daunting task for the visitors and Nick MacLeod's attempt to get them on the board from the halfway line failed to pay dividends.
Flood extended the lead four minutes later after fine work from the forwards brought a penalty in front of the posts after number eight Thomas Waldrom had made an eye-catching dash for the line.
Sale had spent just two percent of the game in the Leicester 22 but they crossed in the 28th minute the line against the odds, after winning a lineout inside their own half Tololima-Auva'a burst away from the ruck before sending on James Gaskell, who fed lock Fraser McKenzie for the score.
MacLeod added the extras and suddenly Sale had a foothold in the match. Julian Salvi was penalised for coming in from the wrong side after a great take from Murphy and MacLeod made it 17-10 with the ensuing penalty.
The unfortunate Thomas was helped off in the 38th minute and Sale's last attempt to make progress towards the Leicester line were thwarted when they knocked on, although they showed enough in the driving rain to suggest a second-half comeback was on.
And sure enough MacLeod was able to narrow the deficit to just four points when Graham Kitchener was adjudged to be offside, the young stand-off slotting the points from 40m out.
Flood re-established a seven-point lead with an easy penalty after an infringement at the ruck, but Sharks continued to press although when Dwayne Peel's clearance kick was charged down inside his own 22 he was lucky to see the ball run out of play with Ed Slater touching down outside the end zone.
And with the Tigers back with the ball in hand they were able to show their class, Flood with a quick offload to Twelvetrees before Murphy and Agulla passed through quicks hands to send Alesana Tuilagi over in the left corner.
Flood was unable to convert from the touchline and Sharks refused to give way, full-back Rob Miller picking it up from deep before evading tacklers and running into the Tigers 22, before the hosts were able to clear from under their own posts.
But the respite did not last long, Gaskell drawing three players before offloading to Tom Brady, who found Miller on the right flank and his pace took him to the line - MacLeod un-erring with the boot again to bring the deficit back to five at 25-20.
There was everything to play for with 15 minutes left, and a 15-phase spell for Tigers came to nothing.
Flood converted a 70th minute penalty after another Sale infringed at the scrum and try as they might, neither team could make any further inroads - Tigers failing to bag a fourth, bonus point try - until MacLeod drop-kicked a three-pointer with the final play of the match, giving the visitors a deserving point.
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