The Tigers scored five tries, the others coming from Fiji winger Vereniki Goneva, lock Graham Kitchener and a penalty try.
Winger David Lemi and centre Alex Grove scored Worcester's tries with former England fly-half Andy Goode kicking 16 points.
Leicester made a blistering start and led 14-3 after just 12 minutes thanks to two sensational tries by Tuilagi. The first came with less than two minutes on the clock after Worcester had won a line-up but got turned over in the Leicester 22.
England fly-half Toby Flood launched a brilliant counter-attack and, after great work by Tom Youngs and Scott Hamilton, Flood fed Kitchener, whose smart change of direction led to Tuilagi's try in the left corner.
Flood converted and, although Goode pulled three points back with a penalty, Goneva had the crowd on their feet with a remarkable counter-attack from one 22 to the other, which led to Tuilagi's second try.
Flood, who had just missed a simple penalty, kicked the conversion from the right touchline but Worcester hit straight back and, after Goode had been denied a try by Geordan Murphy, he slotted an easy penalty.
Flood kicked a penalty to put Leicester 17-6 ahead, and after Goode saved an almost certain try after a mistake by Grove, he kicked his third penalty in the 29th minute.
Worcester full-back Chris Pennell was sin-binned a minute before half-time for a professional foul but his team survived a ferocious onslaught from Leicester who failed to score from several scrums on the line in the closing moments of the half.
Leicester started the second half like they did the first with a try in under two minutes, this time for Goneva, his sixth in five games. It came after Goode had saved Worcester again with a great tackle on Murphy but after Flood's fabulous cut-out pass, Leicester attacked the line and Goneva barged between two players to touch down.
Worcester caught the mood for sensational tries with one of their own in the 49th minute, winger Lemi finishing off a brilliant 80-metre counter-attack with Goode adding the conversion to make it 22-16.
Leicester, however, scored their bonus point try in the 66th minute when referee Andrew Smalling lost patience with Worcester's scrum and went under the posts. Flood kicked the conversion. With nine minutes left, Goode kicked his fourth penalty but Kitchener responded with Leicester's fifth try. Replacement fly-half George Ford missed the conversion.
With the last play of the match, Grove scored Worcester's second try after winning the race to a chip over the top and Goode kicked the conversion.
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