Tuilagi scored the only try of the game but ended on the losing side
Alex Goode scored a late penalty as second-placed Saracens beat Premiership leaders Leicester to close the gap at the top of the table to two points.
Goode (2) and Jeremy Staunton (2) exchanged penalties, before Manu Tuilagi's try edged Tigers ahead.
Staunton and Goode traded kicks again as the home side led 14-9 at the break.
Goode closed the gap to two points with his fourth kick and his fifth won it but Tigers will rue a last-gasp missed penalty from Billy Twelvetrees.
That relatively simple miss from Twelvetrees allowed Saracens to become the first side to win at Welford Road this season and completed the double over the Tigers in the process, following their
26-20 victory at Vicarage Road in October.
Goode opened the scoring with a sixth-minute penalty but Staunton soon levelled in a sloppy opening for both sides.
Saracens had the better of territory and possession and were rewarded by Goode's second penalty after 17 minutes.
Staunton's kick hauled Tigers level for a second time and it brought about a change in fortune for the home side, as they upped the intensity and scored a superb try to take the lead for the first time.
Manu Tuilagi finished off a decisive move involving his brother Alesana along the touchline - the try was confirmed by the video official and, although Stanton missed the conversion, he soon kicked a penalty for a 14-6 lead.
Goode quickly replied with a third penalty of his own to reduce the deficit to five points at half-time.
Hugh Vyvyan came off the bench for Saracens in the second half to break Simon Shaw's Premiership appearance record of 232 but Leicester continued to shade the contest.
Goode kicked his fourth penalty with 15 minutes left to close the gap to two points, before Staunton missed the chance to re-establish the five-point lead.
The miss proved costly as Goode slotted the winning kick with five minutes remaining as Leicester flopped off their feet at a ruck.
There was time for a dramatic finish as replacement Twelvetrees missed the final kick of the game to spark jubilant celebrations among the visiting players.
Leicester boss Richard Cockerill: "We had enough chances to win the game and we didn't take them. We didn't control the ball well enough and it cost us.
"Kickers win you games, they don't lose you games. If Billy kicks that we are having a different conversation. It's not his fault, that's life sometimes.
"The team did not play as well as we needed to across the board. We have a week off next week and then we will have a good week of preparation before we have to go to Bath."
Saracens director of rugby Mark McCall: "We weren't cock-a-hoop in the dressing room. We have played much better than we did today but that is how you have to play against Leicester at Welford Road.
"It was a real arm wrestle, neither side could get away from the other and we just came out on the right end of it.
"We said before the game that there would be moments when they would have the momentum and a lot of teams get overwhelmed by that, and it's important to be able to rise to that."
Leicester: Hamilton; Agulla, M. Tuilagi, Allen, A. Tuilagi; Staunton, Grindal; Ayerza, Chuter, White, Mafi, Skivington, Croft, Newby (capt), Waldrom.
Replacements: Castrogiovanni for White (48), Woods for Croft (65), Hipkiss (for Agulla, 79), Twelvetrees (for Staunton, 79).
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