That score however signalled the start of Munster's period of dominance but despite several assaults on the Ulster line they were unable to cross and the visitors went into the break leading by that early score.
It remained like that until the 67 minute when Steinmetz landed a 40 metre penalty but Munster's response came from Conan Doyle who surged through a gap to score the game's only try that replacement Tadhg Bennett converted.
Steinmetz had the opportunity to put his side back in front but his penalty effort came back off the right upright and Munster to their credit ended the game in the Ulster 22.
Munster: E Ryan; B Carney, K Lewis, T Gleeson, C O'Boyle (T Bennett 65 min); C Doyle (M Kinsella 75 min), M Prendergast (C Sheridan ht); Darragh Hurley, M Essex, T Ryan (D Ryan 64 min); M Melbourne, I Nagle (D Foley 51 min); T O'Donnell, E Grace (J Coughlan 51 min), B Holland capt.
Ulster: J Smith; M Barker, M McCrea, I Whitten, T Seymour; P Sterinmetz, P Marshall; J Carey; N Hanna, B Young; M Wilson, N McCombe; F Paulo, W Faloon, C Henry capt .