Graham Kitchener kept the visitors in the game at half time though, powering over the line against his old club for Leicester's first points of the match shortly before the interval.
Having already had a spell in the sin bin during the first half, Donncha O'Callaghan found himself heading back to the dressing room early in the second half as he collapsed the maul, earning himself a second yellow.
Worcester were reduced to 13 men soon after as Gareth Milasinovich was shown a yellow card just three minutes after coming off the replacements bench.
Leicester made the most of Worcester's discipline issues, with Telusa Veainu closing the gap with a second try of the afternoon for the visitors, before a penalty try inside the final 10 minutes handed the Tigers the lead for the first time in the match.
Lachlan McCaffrey sealed the bonus point and put the win beyond doubt with seconds remaining for Leicester, claiming a chip forward before powering across the line.
The result leaves Leicester second in the table, while Worcester sit 10th following a fourth loss in five matches.