Tries from Lua Lokotui and Fetu'u Vainikolo and 11 points from the boot of Fangatapu Apikotoa earned Tonga a memorable win at Pittodrie.
Greig Laidlaw kicked five penalties for Scotland, who were blunt in attack, as Robinson's men slumped to a third defeat of the EMC Test series following losses to New Zealand and South Africa.
It was an attritional affair on a narrow pitch which limited space and, once again, Scotland's passing lacked the accuracy required as the ball hit the floor with alarming regularity.
Scotland lacked ideas to overcome their physical opponents, who had three players sin-binned but were deserved winners as the hosts tasted defeat in Aberdeen for the first time.
A season which featured early World Cup elimination and a RBS 6 Nations wooden spoon was revived by the June wins in Australia, Fiji and Samoa before New Zealand and South Africa inflicted defeats which will see Scotland outside the top eight seeds for the 2015 World Cup draw.
Assuming he is retained, Robinson will next enter his fourth Six Nations, beginning with the Calcutta Cup at Twickenham, needing a remarkable turnaround to avoid another abject spring showing.
Due to a mixture of choice and circumstance, change was required for the final match of 2012, with six alterations from the XV which began the Springboks Test.
Scrum-half Henry Pyrgos and loosehead prop Kyle Traynor made their first starts for Scotland in the EMC Test with Tonga in Aberdeen.
Pyrgos and Traynor were two of six changes from the Scotland side beaten 21-10 by South Africa last weekend, with hooker Scott Lawson, lock Alastair Kellock, flanker Alasdair Strokosch and centre Max Evans also selected to start at Pittodrie, while uncapped trio Grant Gilchrist, Tom Heathcote and Gordon Reid were among the replacements.
Tonga made a solitary change from their last outing, last week's 22-13 defeat of the United States in Colwyn Bay, with Hale T-Pole selected at flanker in place of Leicester's Steve Mafi.
It was the third Test between the sides and Scotland were bidding for a handsome win, just as they claimed in 1995 and 2001, while the visitors were eager to prove their strength after beating France in the World Cup.
Fangatapu Apikotoa missed an early penalty from 45 metres before kicking a second from in front of the posts after Scotland killed the ball.
Greig Laidlaw had an opportunity to level, but his penalty attempt careered back off the post before Scotland countered and earned a lineout five metres out.
Scotland drove forward and Laidlaw kicked the hosts level when an infringement was spotted amid ferocious Tonga defence.
The narrow pitch limited space and twice in successive moves loose Scotland passes hit the floor to bring progress to an abrupt halt.
Tim Visser and Sean Lamont stretched Tonga down the left and the pressure brought a cynical penalty as Sukanaivalu Hufanga fell over the ball at a ruck.
Laidlaw kicked for the corner and Scotland's forwards rolled towards the line and over. Referee Mathieu Raynal sought the opinion of the television match official but Carlo Damasco decided the evidence was inconclusive and Scotland had an attacking scrum.
Scotland were camped deep in Tonga's 22 but could not penetrate the red defensive wall before turning the ball over.
A gap then opened up in front of Laidlaw and he ran 30 metres towards the Tonga line.
Visser was on his left shoulder, but marked, and Strokosch was on his right, but the flanker fumbled Laidlaw's pass as defenders recovered and Tonga soon reclaimed possession to end the danger.
Tonga continually infringed at the breakdown and Raynal lost patience when lock Lua Lokotui obstructed Richie Gray at a lineout and was sent to the sin-bin.
Prop Halani Aulika was fortunate not to join him after body-checking Matt Scott, with no attempt to tackle using his arms.
Tonga's short-handed scrum were penalised for bringing down a set-piece and Laidlaw's kick was successful to give Scotland a half-time lead.
Scotland's lack of progress was epitomised when number eight David Denton - in the side to spark momentum with his ball carrying ability - was pushed 10 metres backwards by a double tackle.
Lamont did provide a spark, returning a kick by slaloming 40 metres towards the line.
He lacked support, but Tonga strayed offside, presenting Laidlaw with another shot at goal. The Edinburgh captain's kick was successful, stretching the lead to six points.
Scotland attempted to counter Tonga's vicious rucking, but transgressed. Apikotoa missed the resulting penalty shot at goal.
The visitors kept the ball tight and made good progress towards the Scotland line, only for a handling error from Vainikolo to stop them short.
Tonga's persistence paid off when they spread the ball wide and Lokotui made amends for his earlier indiscretion by burrowing over after 53 minutes. Apikotoa converted to put Tonga 10-9 ahead.
Another penalty was conceded by Tonga in front of the posts and Laidlaw put the hosts two points in front.
Laidlaw kicked his fifth penalty to hand Scotland a five-point advantage inside the final quarter of the contest.
Apikotoa reduced the deficit with his second penalty kick before Tonga took the lead once again.
It was all too easy as the ball was spread wide to Vainikolo, who simply stepped up the pace and ghosted down the left, evading substitute Nick De Luca, to score.
The conversion was missed by Apikotoa and Heathcote came on for his debut.
Nili Latu became the second Tongan sin-binned 11 minutes from time for leaping on top of a maul, but Heathcote's resulting penalty was short.
Apikotoa kicked his third penalty to leave the hosts requiring a converted try to win with six minutes left.
It was a tall order for any side, but Scotland's chances increased when replacement Sione Timani was sin-binned.
Tonga survived with 13 men before Latu returned, with Scotland handed an attacking scrum as the game ticked into added time.
Scotland pushed forward but captain Kelly Brown lost control at the base of the scrum and Tonga scrambled clear.
The last act of the game was Heathcote dropping a Rory Lawson pass as Scottish players stood crestfallen - and defeated - across the pitch.