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George Ford had a solid first half with the boot, converting both tries as well as adding two penalties and a drop goal to send Bath to a 23-0 lead.
The home side continued to dominate after the break, as Kyle Eastmond dived over following a quick counter-attack by Bath, while Peter Stringer and Olly Woodburn also got themselves on the scoresheet.
Things got worse for the visitors in the final minutes as Mele was dismissed for a stamp on Rob Webber.
The result moves Bath to the top of the table, while Leicester sit fourth.