A magnificent try from Leicester centre Manu Tuilagi separated the sides at the break as three penalties apiece from Jeremy Staunton and Alex Goode saw the hosts hold a 14-9 interval lead.
But the Tigers remained scoreless after the break and two more Goode penalties, the second just five minutes from time, saw Saracens become the first side to win at Welford Road in the league this season.
Leicester had a late chance to snatch a 10th-straight league win but Twelvetrees, just on from the bench, pushed his effort wide with time up to spark jubilant celebrations among the visiting players.
Gloucester, meanwhile, completed a season's double over fierce local rivals Bath and underlined their credentials as genuine title challengers in the process with a 34-22 success.
A ninth successive win in all competitions - Gloucester's longest unbeaten run since 2002 - was secured by tries from England prop Paul Doran-Jones, centre Henry Trinder and wing Tom Voyce's double at Kingsholm
Fly-half Nicky Robinson added four penalties and a conversion, while Matt Banahan, Tom Biggs and Ben Williams scored for Bath - but the visitors could have few complaints as they suffered just a second defeat from their last 10 starts.
And a miserable day for Bath ended when their England international centre Olly Barkley, who had earlier landed a penalty and conversion, was carried off nursing what appeared to be a serious leg injury.