Burke - who has now kicked 86 points this season - clipped over a ninth minute strike as Munster withstood a second half onslaught from the westerners, and the 51st minute sin-binning of hooker Jerry Flannery, to record their ninth straight win.
It was the sides' second 3-0 scoreline in the space of twelve months - the rested Ronan O'Gara kicked the sole penalty in Munster's win at Dubarry Park, Athlone last January.
Connacht, meanwhile, who are staring into difficult trips to both Ulster and Grenoble early next month, are still without a win over their southern rivals since their 11-9 Interprovincial success in 1986/87.
Monday, December 27Connacht 0 Munster 3, The SportsgroundScorers: Munster: Pen: Paul Burke
(15) Matt Mostyn(14) Ted Robinson(13) Darren Yapp(12) James Downey(11) Conor McPhillips(10) Paul Warwick(9) Tom Tierney(1) Ray Hogan(2) John Fogarty(3) Peter Bracken(4) Christian Short(5) Andrew Farley (Capt)(6) John Muldoon
Replacements used: Bernard Jackman and Eric Elwood for Fogarty and Robinson (both 59 mins), Michael Swift for O'Sullivan (65), Chris Keane for Tierney (73). Not used: Tony Buckley, Pieter Myburgh, Justin Meagher.
(15) Christian Cullen(14) Paul Devlin(13) James Storey(12) Jason Holland(11) Anthony Horgan(10) Paul Burke(9) Eoin Reddan(1) Marcus Horan(2) Jerry Flannery(3) John Hayes(4) Donncha O'Callaghan(5) Paul O'Connell(6) Stephen Keogh(7) Denis Leamy(8) Anthony Foley (Capt)
Replacements used: Frankie Roche for Horan (36 mins-half-time), Roche for Leamy (51-61 mins), Shaun Payne for Storey (60), Mike Prendergast and Alan Quinlan for Reddan and Keogh (both 64). Not used: Mike Storey, Trevor Hogan, Mossy Lawlor.
Referee: Simon McDowell (IRFU)