Dominating at the scrums and the breakdown Glasgow were rewarded with a series of penalties with Dan Parks duly converting.
Peter Stringer was sinbinned just at the halfway mark and Munster have it all to do in the second half to turn the 12-3 deficit around.
Munster : F Jones; D Howlett, T Gleeson, L Mafi, D Hurley; J Manning, P Stringer; M Horan, D Fogarty, T Buckley; M O'Driscoll capt, D Ryan; B Holland, N Ronan, D Leamy. Replacements: D Varley, J Brugnaut, T O'Donnell, J Coughlan, T Morland, S Deasy, B Murphy.
Glasgow : B Stortoni; R Dewey, P Murchie, G Morrison, T Evans; D Parks, C Cusiter; J Welsh, D Hall, M Low, T Barker, A Kellock (capt), K Brown, J Barclay, J Beattie. Replacements: P MacArthur, K Tkachuk, D Turner, R Vernon, M McMillan, R Jackson, C Shaw.