The home side clawed their way back into the game and dominated territorially and out-half Joe Carlisle reduced the deficit with a penalty after a good break by Ollie Winter forced Munster to stray offside.
Just before half-time, off the top lineout ball was spread wide for Tom Gleeson to score in the corner and Ian Nagle scored their bonus point try shortly after the restart.
Coventry who had been guilty of poor defence in the opening half scored two push-over tries in the second half, the second after six minutes of added time to claim a bonus losing point.
Munster. F Jones; D Barnes, T Gleeson, S Deasy, D Hurley; D Cusack, D Williams; J Brugnaut, M Sherry, S Archer; I Nagle, D Foley; N Williams, N Ronan, J Coughlan capt. Replacements: S Henry, D Kilcoyne, D O'Callaghan, P O'Mahony, A Burke, P Rowley, S Zebo.
Coventry: O Winter; S Frewin, J Lewis, C Lewis, W Hurrell; J Carlisle, M Walls; K Davis, R McMillan, R Dugard; A Brenton capt, L McGowan; S Herrington, R Bignell, H Venter. Replacements: J Merrigan, S Roberts, J Hall, B Dechartres, D Locke, J Thomas, P MacKenzie.