Borders end the season in last place, with just 22 points from 22 games played.
And it was a sad exit for former Scotland hero Gary Armstrong, who was forced off with a first-half leg injury.
Borders got off to a bright start as Gareth Morton fired over a sixth-minute penalty after Munster crept offside in midfield.
But the province hit back strongly to grab the initiative. First, Jeremy Staunton levelled the contest when a home forward entered the ruck from side on.
Then wing Anthony Horgan pounced on turnover ball to cruise over for the opening touchdown. Staunton added the conversion.
Borders suffered a double blow from which they never recovered. They fell further behind when Anthony Foley was driven over for Munster's second try, Staunton keeping up his fine kicking record.
Then Armstrong's premature departure prompted a richly-deserved standing ovation from both sets of fans - even though he could barely stand himself.
Munster kept up the pressure, but Borders proved stubborn in defence. And the Irishmen had to rely on another Staunton penalty early in the second half to get their score moving again.
The Scots replied in stirring style with rookie Ian Berthinussen bagging a fine try, converted by Morton to keep the contest open.
Borders carved out a series of late chances, but a combination of errors and strong Munster defence kept them out.
Scorers: Borders (10) Try: Berthinussen Pen: Morton Con: Morton
Munster (18) Tries: Horgan, Foley Con: Staunton Pens: Staunton (2)
Morton, N. Walker, Berthinussen, Utterson, Cranston, Vili, Armstrong, Cross, Scott, Douglas, Weir, Stewart, MacLeod, Sititi, K. Brown.
Replacements: Ford, Johnston, Davidson, Dalziel, Fairley, MacRae.
Cullen., Payne, Mullins, Holland, Horgan, Staunton, Reddan, Horan, Flannery, J. Hayes, Pusey, O'Connell, Quinlan, Foley, Wallace.
Replacements: Roche, McIlwham, Hogan, S. Keogh, Callaghan.., Prendergast, Touhy.