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A cagey opening spell saw Andy Goode and Ignacio Mieres exchange penalty kicks before Matt Mullan found the try line in the 29th minute, giving Wasps an 11-9 lead at the break.
The home side built on their lead at the start of the second half, and Christian Wade and Jake Cooper-Woolley added tried within 10 minutes of the restart.
Josh Drauniniu looked to have brought Worcester back into contention with 15 minutes left to play, scoring the visitors' first and only try of the afternoon, but Guy Thompson was able to add a further score for the hosts, sealing the victory.
The result leaves Wasps eighth in the table, while Worcester are bottom.