The 30-year-old Paterson provided all his side's points in a close contest that eventually ended with the Pumas making it seven wins in a row over the team they last conquered in the quarter-finals of the 2007 Rugby World Cup.
The fourth of Paterson's penalty haul not only took him past Hastings' record mark of 667 points, but actually gave Scotland the lead 12-10 after 56 minutes. His final kick extended the lead and took his Scottish tally to 671.
Trailing 15-10, Todeschini banged over two more penalties to restore the home side's lead before an injury time try from Gonzalo Tiesi saw the third ranked team in the world home to a slightly fortunate victory.
Todeshini and Paterson had exchanged early penalties before Alvaro Tejeda scored a try from close range on his debut. Todeshini's conversion made it 10-3, but Paterson's boot chipped away at the home lead until it was just a single point at the break.
Those three penalites took Paterson's run of successful successive goal kicks to a remarkable 36 before he finally missed one just before half-time.
The two teams move on to Buenos Aires for Saturday's second Test, when Paterson will be hoping to become the sole owner of the Scottish cap record.