The win also moved Scotland up two places on the IRB World Rankings. They leapfrogged both Wales and Argentina to reach their highest position since November 2006 of sixth place.
A first test try by lock Jim Hamilton set the Scot on their way and the boot of Dan Parks did the rest of the damage as the tourists backed up their RBS 6 Nations triumph over Ireland at Croke Park, as well as their uncapped victory over Japan Select, with a stunning 2-0 series win over the Pumas.
That Hamilton score came after only two minutes and tone for another set the tone for another great forward effort from skipper Ali Kellock's pack as they tamed the Pumas in their own back yard.
Once again Parks, who scored all 24 points in Tucuman, was the chief architect of the home side's downfall and he converted Hamilton's try to make it 7-0. Felipe Contepomi hauled back three points with a penalty.
There wasn't too much for the 30,000 home crowd to shout about, although a second Contepomi penalty cut the gap to a single point. But a yellow card to prop Rodrigo Roncero gave the Scots an advantage before the break and a penalty from a metre inside his own half by Parks made it 10-6 at the break.
The third quarter remained a stalemate before Rodriguez, taking over the goalkicking from his skipper, made it 10-9 with a penalty. That set up a rousing final 20 minutes in which Parks kept his cool to slot another penalty to give him 32 points over the two games and 89 points in six Tests this year.
"If you had asked anybody before the Croke Park game if we would win four on the bounce they would have said no," said Scottish skipper Kellock.
"We now feel we can win any game. In saying that there is world-class opposition out there and they are only going to get stronger and stronger."
15 Hugo Southwell (Stade Francais)
14 Sean Lamont (Scarlets)
13 Max Evans (Glasgow Warriors)
12 Graeme Morrison (Glasgow Warriors)
11 Simon Danielli (Ulster)
10 Dan Parks (Glasgow Warriors)
9 Rory Lawson (Gloucester) vice-captain
1 Allan Jacobsen (Edinburgh)
2 Ross Ford (Edinburgh) s
3 Moray Low (Glasgow Warriors)
4 Jim Hamilton (Edinburgh)
5 Alastair Kellock (Glasgow Warriors) CAPTAIN
6 Kelly Brown (Glasgow Warriors)
8 Johnnie Beattie (Glasgow Warriors)
7 John Barclay (Glasgow Warriors)
16 Scott Lawson (Gloucester) for Ford, 67 min
17 Alasdair Dickinson (Gloucester) for Jacobsen, 60 min
18 Scott MacLeod (Edinburgh) for Kellock, 66 min
19 Alasdair Strokosch (Gloucester) for Beattie 62 min
20 Mike Blair (Edinburgh) for Lawson 69 min
22 Nick De Luca (Edinburgh) for Evans, 71 min
21 Phil Godman (Edinburgh)