Converted tries from Ben Herring and Dale Rasmussen plus a penalty apiece from Paul Burke and Shane Drahm meant it was 10-10 after half an hour.
Burke's penalty edged Leicester ahead and soon after the re-start Ollie Smith raced over from 50m for the Tigers.
Benjamin Kayser's try made the game safe and Drew Hickey's converted try was just a consolation for Worcester.
Leicester head coach Richard Cockerill:
"I would have liked us to have played better, but it was a good result and keeps us in the mix. We worked very hard and scored some nice tries. "Worcester are a difficult side to play against. They are not missing any players and it was a good win for us. "We would have settled for four wins out of six during the
World Cup.
"We have suffered more than any other club during this spell and we have come through it very well. We will only get stronger."
Worcester director of rugby Mike Ruddock:
"It's just not happening for us at the moment and it's disappointing because I thought we were the better side.
"We tried to play rugby and our two tries were as good as you will see, but silly errors meant we were chasing the game.
"We gave away a couple of bizarre tries and put ourselves under pressure.
"Uncontested scrums is not what the game is all about. It devalues the game and I think we need to look at making teams have two props on the bench."
Leicester: G Murphy; J Murphy, Smith, Vesty, Rabeni; Burke, B Youngs; Stankovich, Kayser, Castrogiovanni, Hamilton, Deacon, Wentzel, Herring, B Deacon.
Replacements: Davies, Young, Abraham, Crane, F Murphy, Cornwell, Varndell.
Worcester: Drahm; Garvey, Rasmussen, Tucker, Delport; Crichton, Powell; Morris, Lutui, Taumoepeau, Bowley, Gillies, Hickey, Sanderson, G Quinnell.
Replacements: Windo, Gotting, Murphy, Horstmann, Powell, Brown, Benjamin.
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