Manu Tuilagi put the hosts ahead following a turnover in the Leicester 22. The ball was shipped though six pairs of Leicester hands for Tuilagi to burst over.
Tuilagi added his second 10 minutes later, as Fijian Veriniki Goneva made a 50-metre break to set up the score.
Nine points from the metronomic boot of Andy Goode kept Worcester in the game, setting the score to 17-9 at half time.
Goneva added one of his own early in the second half, before Denis Lemi pulled one back for Worcester.
The boot of Andy Goode continued to tick over but a late Alex Grove try was cancelled out by a Graham Kitchener score as Leicester sealed a 34-26 victory.