The sides were locked at 16-16 at half-time with both teams scoring a try and three penalties.
Leicester went ahead just after the break when Alesana Tuilagi crossed on 46 minutes but Worcester took the lead with two penalties from Shane Drahm.
And the Tigers sealed victory when Matt Cornwell crossed on 62 minutes.
The game was watched by England coach Andy Robinson, who will be pleased with the news that all his players came through unscathed ahead of the match with Scotland next weekend.
Worcester assistant coach Anthony Eddy:
"We came here expecting to perform and hoping our performance was good enough to win. "Unfortunately today it wasn't quite good enough. But we have got to be pleased with the effort we put in for 80 minutes, and I'm pretty proud of the way we stood up here on their home ground.
"We've worked hard this week - and although we didn't get the result on the scoreboard, the result for us is knowing we can compete with the best of them."
Leicester: Murphy; A Tuilagi, Cornwell, Smith, Varndell; Goode, Ellis; Holford, Chuter, White; Hamilton, Cullen; Moody, Jennings, Corry.
Replacements: Bemand for Ellis (65), Morris for Holford (57), Taikaufa for Chuter (73), B Deacon for Hamilton (51).
Not Used: Johnson, Humphreys, Dodge.
Worcester: Le Roux; Trueman, Rasmussen, Lombard, Tucker; Drahm, Gomarsall; Windo, Hickie, Tuamoepeau; Murphy, Gillies; Horstmann, Harding, Hickey.
Replacements: Whatling for Tucker (73), Vaili for Hickey (51).
Not Used: Van Niekerk, L Fortey, O'Donoghue, Powell, Hylton.
Sin Bin: Tucker (45).
Att: 16,815
Referee: David Rose (RFU).