Ireland went into this one with 10 straight wins over the Scots but they seemed set to share the spoils until they conjured a winner from a tapped penalty in the dying seconds.
In the process, Murphy ensured a first ever bonus point for Ireland in a Six Nations game as they had already chalked up three prior to that.
It was rough justice on a Scottish side who looked set to get their first win in six seasons and who at least deserved a share of the spoils.
It was obvious in the early stages that Ireland’s perfect record against the Scots was under threat as the home side took the game to them from the outset on a bitterly cold and wet night at Broadwood Stadium north of Glasgow.
Scotland’s best ever points tally in a match against Ireland was the dozen they got in a 45-12 drubbing in Donnybrook last year but they surpassed that by half-time last night when they deservedly opened up a 15-10 lead.
The Scottish has been improving over the past year or more since Ireland’s record 73-3 win here a couple of season’s ago and the first ever full-time Scots professional in the women’s game laid down a marker with a couple of tries in the opening half.
Jade Konkel missed the November series through injury but the impressive No.8 marked her return by twice punishing the Irish.
She struck for the opening score after five minutes when Scotland piled on the pressure after a good break by flanker Louise McMillan, with Sarah Law making it 7-0 to a Scottish side looking for their first win in the tournament since 2011.
The superb passing of debutant scrum-half Ailsa Hughes gave Ireland a foothold while Sene Naoupu and Jenny Murphy cracked holes in the home defence.
And it was Naoupu who crowned her birthday this weekend with Ireland’s opening try after 11 minutes when she finished a good move in the left corner. Ireland’s dominant scrum gave them an edge but they didn’t always convert this into scores despite a series of five-metre efforts.
But they got the lead from one of them after going wide and while Naoupu was held up under the posts, quick ball to the left was finished by Alison Miller.
Nora Stapleton and captain Paula Fitzpatrick were held up short as Ireland piled forward, but Scotland held out and they went back in front eight minutes from the break when a penalty to the left corner was finished with a good lineout drive which yielded a second try for Konkel.
Law was unable to convert but she made no mistake from a 30-metre penalty just before the break to leave Scotland 15-10 in front at the interval.
Ireland stepped up a gear after the restart and good pressure saw Scottish tighthead Lindsey Smith binned and when Ireland went to the right corner they got the drive off the lineout and loosehead Lindsey Peat got the touchdown to level the match.
Stapleton was unable again to convert from the right and there were a couple of let-offs for the Irish at the other end as first Law missed a penalty and then when out-half Helen Nelson took over the kicking, she too was off target with a penalty from just to the left on the 22.
That left the sides deadlocked at 15-15 going into the final 10 minutes with Scotland growing in confidence, backed on by the home crowd.
But then Ireland staged one final effort and when a lineout penalty was repelled, Ireland tapped and went and when replacement prop Ciara O’Connor was stopped, Mary Healy spread it quickly and Murphy crashed over for the winner.
Tries: J Konkel (2). Conversion: S Law. Penalty: S Law.
Tries: S Naoupu, A Miller, L Peat, J Murphy. Conversion: N Stapleton.
C Rollie; M Gaffney, L Thomson, L Martin, R Lloyd; H Nelson, S Law; T Balmer, R Malcolm, L Smith; E Wassell, D McCormack; K Dunbar, L McMillan, J Konkel.
L Park for Malcolm (38), K Dougan for Konkel (60-62), S Bonar for McCormack (62), J Maxwell for Law (62), H Lockhart for Balmer (67).
M Coyne; N Kavanagh, J Murphy, S Naoupu, A Miller; N Stapleton, A Hughes; L Peat, L Lyons, A Egan; O Fitzsimons, ML Reilly; C Griffin, C Molloy, P Fitzpatrick.
E Anthony for Fitzsimons (h-t), E Considine for Kavanagh (h-t) M Healy for Hughes (69), J Finlay for Lyons (71), I Van Staden for Peat (71), C O Connor for Egan (71).
Aimee Barrett-Theron (South Africa)