J McKinney 1 Converions, 3 Penalties
L O'Dea 1 Try
J Cronin 1 Try
S Henry 1 Try
Rotherham opened their scoring with a try from scrumhalf Jimmy Williams and James McKinney kicked three penalties in the opening 40.
Munster started the stronger using their experienced backline to get the ball moving, making the yards and the offloads, and they were rewarded with a penalty after 6 minutes which Deasy kicked.
But within minutes the home side returned with a try when scrumhalf Williams dotted over the line, McKinney missed the conversion.
A period of forward pressure from the Munster scrum resulted in the referee awarding a penalty try after 20 minutes, giving Deasy the kickable conversion in front of the posts.
Two penalties from McKinney gave his side the advantage again before Luke O'Dea claimed a great individual try putting Munster on the front foot after 35 minutes. The margin was reduced to a point just before the half with McKinney adding his third penalty.
Munster continued to expose the Rotherham defence and poor tackling with second half tries coming from James Cronin on his B&I Cup debut, captain Sean Henry and Scott Deasy.
Deasy spotted a wayward Rotheram pass and took advantage scoring an intercept try under the posts on the 65 minute mark. He also added the three conversions.
As the game closed out Munster's discipline dropped with Philip Donnellan and Ian Nagle yellow carded and Rotherham piled on the pressure with Munster down to 13 men. They were rewarded with a final penalty try with the advantage in the scrum and it was converted by McKinney to give a fulltime score of 21-36 in Munster's favour.
Titans now travel to Cork for round 4 in Musgrave Park on Friday night, ko 6.30pm.
Munster: Denis Hurley (Ronan O'Mahony 51); Luke O'Dea, Danny Barnes, Ivan Dineen, Johne Murphy; Scott Deasy (Johnny Holland 70), Cathal Sheridan (Brian Slater 78); James Cronin, Sean Henry Capt. (Duncan Casey 64), John Ryan (Christy Condon 66); Dave Foley (Philip Donnellan 70), Ian Nagle; Brian Hayes, Ryan Murphy, Shane Buckley (Jack O'Donoghue 39). Replacements: Duncan Casey, Christy Condon, Philip Donnellan, Jack O'Donoghue, Brian Slater, Johnny Holland, Ronan O'Mahony
Rotherham Titans: Fergus Mulchrone Capt.; Peter Homan, Joel Gill, Pale Nonu, Ed Styles, James McKinney, Jimmy Williams, Shane Cahill, Ted Stagg, Gareth Denman, Toby Freeman, Nile Dacres, Latu Makaafi, Joe Ellyatt, Rory Pitman. Replacements: Marshall Gadd, Ross Davies, Dan Sanderson, Alex Rieder, George Oliver, Garry Law, Charlie Mulchrone.