The first round tie at Park Lane was a forwards-dominated affair, but the hosts showed the ability of their backs when they struck for a well crafted try in the eighth minute. This preceded a try from Arklow winger Joni Butterworth who got over in the corner with Duggan failing to add the extras.
Territory was shared for much of the first half, but Leinster managed to add to their tally as half-time approached.
Munster spilt possession in their 22 and Coolmine full-back Niall O'Donoghue gobbled it up to score from close range, with his unconverted try widening the gap to 13 points.
With a strong wind behind them, Munster made immediate headway in the second half and an impressive 46th minute penalty from Old Christians' Stuart Lee got them off the mark.
Leinster missed an opportunity to respond off the kicking tee and the visitors, with Newcastlewest second rower James Corbett standing out in the pack, closed the gap to five points after Waterpark's Eoin Duffy crossed the whitewash.
It was a deserved score after some fine phase-building and ball retention by the defending champions however, the conversion was missed in the windy conditions and Leinster, thanks to some gritty defence late on, stood firm to record a hard-fought win.
Munster had some star performers in the pack which included Corbett and No. 8 Ian Fitzgerald.
A stand out performance also came from try scorer Duffy giving John O'Neill's side confidence going into their first home game this Saturday, 3rd May when they take on Ulster at Youghal RFC (kick-off 2.30pm).
Ulster will be hoping to continue on a winning streak following their 62-6 defeat over Connacht last Saturday in Larne RFC.
MUNSTER: Eoin Duffy (Waterpark); Warren Kelly (St. Senan's), Mark Chandler (Cobh Pirates), Darren O'Keeffe (Crosshaven), Eoin O'Carroll (Tralee); Stuart Lee (Old Christians), Aaron Daly (Youghal); Pa Ryan (St. Senan's), Mike Cronin (Castleisland) (capt), Hugh Carolan (Waterpark), Darragh Joyce (Waterpark), James Corbett (Newcastlewest), Dave McCormack (Clanwilliam), Dave O'Donoghue (Waterpark), Ian Fitzgerald (St Senan's).
Replacements: Dave Fitzgerald (Waterpark), Mike Calnan (Skibbereen), Aidan Foley (Clonakilty), Aaron Skerritt (St. Senan's), Eoin Geary (Cobh Pirates), Mark Healy (Kanturk), Eoin O'Dwyer (Thurles), Cian Keegan (Skibbereen).
LEINSTER: Niall O'Donoghue (Coolmine); Killian Everard (Kilkenny), Ben Swindlehurst (Newbridge), Richie Forbes (Malahide), Joni Butterworth (Arklow); Bill Duggan (Monkstown), TC Campbell (Dundalk) (capt); James Clifford (Monkstown), Johnny Lee (Coolmine), Dylan Quinn (Longford), Niall Smullen (Wicklow), Geoff Mullan (Coolmine), Paul Gallogly (Longford), David Gilchrist (Coolmine), Dave O'Connor (Kilkenny).
Replacements: Kevin McCarthy (Newbridge), Cathal Bannon (Portarlington), Cian Carroll (Monkstown), Barry Stewart (Longford), Damien Broughall (Cill Dara), Gavin Kennedy (Ashbourne), Chris Jebb (Clondalkin), Colm Glynn (Longford).
Munster Juniors Fixtures
Sat. 3rd May, Munster v Ulster, Youghal RFC, ko 2.30pm
Sat. 10th May, Munster v Connacht, Presentation RFC, ko 2.30pm