Munster are only one of four sides in the competition who remain unbeaten. They looked in serious trouble at half time on Saturday when they trailed 12-0 thanks to four penalties from former Welsh international Arwell Thomas.
However, whatever Anthony Foley and Ian Costello had to say during the half-time 'chat' found receptive ears and that plus the introduction of Billy Holland had the desired effect.
Declan Cusack kicked two penalties and then added the conversion to captain Peter O'Mahony's try for Munster to edge ahead. Tom Gleeson scored Munster's second try and although Cusack missed that conversion he made amends with his third penalty just before the end.
Munster: D Riordan; D Barnes, T Gleeson (J Manning 59th min), S Deasy, C O'Boyle; D Cusack, D Williams (C Murray 76th min); D Kilcoyne, S Henry (G Slattery 78th min), S Archer; D Foley, I Nagle (N Melbourne temp); S Hassett (B Holland 41st min), P O'Mahony capt (N Melbourne 72nd min), N Williams.
Neath: K Morgan; K James, S Thomas, N Brew, A Jenkins; A Thomas (G McCarthy 69th min), K Farrell (T James 78th min); N Downs (E Lewis 78th min), A James (G Price 65th min), M Jones; E Evans, N Edwards; M Collins (C Price 62nd min), L Evans, G Gravell.