At the windy Crosshaven venue, it was Leinster who opened the scoring with a penalty from Nora Stapleton in the eighth minute but a quick response from Niamh Briggs had the sides level two minutes later.
When a scrum collapsed, midway through the half, Briggs again showed initiative to kick a penalty to put Munster 6-3 ahead.
From the kick-off, Munster captain Joy Neville recycled the ball to full-back Briggs who launched it in to the Leinster 22 but Munster could not make further ground and when play turned over, the hosts conceded a second penalty which full-back Stapleton converted.
With the sides level and five minutes remaing of the first half, Briggs converted a third penalty and the score was to prove to be the last and most crucial of the game.
Leinster kept themselves firmly in Munster territory for a large part of the second half, but an impressive defensive effort and significant performances from Fiona Hayes, Louise Austin and Nicole Fitzgerald ensured that the champions held on to their slender lead.
Manager Regina O'Reilly was thrilled with the dogged determination shown by the Munster team and praised Hayes, Austin and Fitzgerald in particular for their consistency.
"Niamh Briggs did the business for us in the first half with the penalties but we were lucky to have that lead at half-time," she said.
"We were under severe pressure in the second half but the girls were 100% focused and never deviated from the plan.
"Leinster are our greatest rivals so to speak and it's always down to the wire, so to keep grafting out victories is something that gives us great confidence looking to our next game against Connacht and the Interpro finals at Donnybrook on November 29."
Meanwhile, Connacht picked up their first win in the competition last Saturday. Coached and managed by Angela Flaherty, Sinead Cosgrave and Lyndon Jones, the westerners grabbed tries through Alison Miller and Clare Molloy as they beat Ulster 12-0 at Ravenhill.
Miller, Molloy, Edel Durkin, Clare Rafferty and Eugenie Fritsch all impressed for the visitors as they recovered well from a heavy defeat to Leinster in the opening round.
Despite the best efforts of number 8 and captain Diane Nixon, Ulster were 7-0 down at the break and they were left frustrated when a number of forward drives into the Connacht 22 failed to result in scores.
Connacht's clever attacking lines and free-flowing style had Ulster under pressure late in the opening half and only last ditch tackles from Brenda Brogan and Nikita Armstrong kept the Ulster line intact.
After a heavy rain shower, the second period saw Connacht continuing to impress out wide with Ulster maintain their dominance in the forwards.
But after an unconverted try, Connacht stepped it up a gear in the forwards and their back row, in particular, came to the fore. In the end, the visitors ran out deserved winners.
RESULTS SO FAR -
Munster 46 Ulster 0, Thomond Park Stadium; Leinster 33 Connacht 8, Donnybrook Stadium
Munster 9 Leinster 6, Crosshaven RFC; Ulster 0 Connacht 12, Ravenhill
FIXTURES TO COME -
Ulster v Leinster, City of Derry RFC, Saturday, November 14, 2.30pm
Connacht v Munster, The Sportsground, Saturday, November 14, 2pm
Women's Interprovincial Finals, Donnybrook, Sunday, November 29, kick-offs tbc