They took the lead with an early Ian Humphreys penalty and subsequently never lost the lead.
Ronan O'Gara levelled with a 25th minute penalty but Leicester scored the first of their two tries when Geordan Murphy went over in the right hand corner in the 28th minute.
O'Gara reduced the deficit with an injury time penalty to leave his side trailing by just two points at the break. (8-6)
Munster's performance improved in the second half but the Leicester defence was superb and they extended their lead with an Ollie Smith try with about 13 minutes of normal time remaining. Huumphreys was well wide with the conversion but in the ene it made no difference.