Alvaro Cejudo, Armenteros and Roberto Torres all struck during a sensational opening half in Pamplona as the visitors blew their chance to climb above Barcelona into second.
The hosts made a stirring start in Pamplona, deservedly taking the lead just six minutes in through Alvaro Cejudo.
Emiliano Armenteros added a sensational second approaching the midway point of a shockingly one-sided first half and Roberto Torres effectively put the game to bed with his effort shortly before the break.
After losing to Almeria early this month, Atletico suffered its second defeat from its last three league games to raise more doubts over the club's title credentials.
And up next is the visit of neighbors Real next Sunday, with the performance against Osasuna suggesting Diego Simeone's side will need to significantly improve at a key juncture in Atletico's season.
Left back Filipe Luis returned to Atletico's starting lineup following a thigh strain, but coach Simeone rested key trio Miranda, Arda Turan and Koke, with all three starting on the bench.
Osasuna got off to the perfect start and took the lead within six minutes as the unmarked Cejudo turned in Armenteros' deep corner after arriving late at the back post.
Mario Suarez was in the right place at the right time four minutes later as Cejudo's right-wing cross looked destined to be knocked in by Oriol Riera, but the Atletico midfielder flicked it away with an important header.
Atletico was punished again after 21 minutes, however. Armenteros was given too much time and space about 25 yards from goal and the Argentine belted an unstoppable drive past the powerless Thibaut Courtois.
With halftime approaching quickly, Torres amazingly put the hosts three up as he burst between Diego Godin and Toby Alderweireld to head Damia's cross into the bottom-left corner.
Atletico was almost gifted a way back into the contest in the 57th minute as Jordan Loties sliced Filipe's cross toward his own goal, but luckily for Javi Gracia's men it flew just wide.
Simeone had made all three of his changes by the 61st minute as Koke, Turan and former Osasuna star Raul Garcia all came on, but still Atletico struggled to cut through a well-organized defense.
Cejudo should have scored a second 18 minutes from time as Riera looped a pass over Godin for the winger, but his first touch was poor and his eventual shot only found the side netting.
Atletico nearly pulled one back through Garcia in the 77th minute as he volleyed Koke's delivery wide from a tight angle but Osasuna held on to crank up the pressure on Simeone and his players heading into next weekend's Madrid derby.