The Jaguares' seven-match Super Rugby winning run ended Saturday in a 43-34 loss to Northern Bulls after an 11-try festival in Pretoria.
Defeat virtually ended Argentine dreams of winning the South African conference and a late conversion rebounded off the post, robbing them of even a bonus point.
The result left the Jaguares three points behind leaders the Golden Lions, who will win the conference for a third consecutive year if they beat the Bulls in Johannesburg next Saturday.
There was a silver lining for the Buenos Aires outfit, though, as they were guaranteed a knockout-phase place when Coastal Sharks later fell 27-16 to Western Stormers in Cape Town.
It will be Jaguares' first appearance in the play-offs after debuting in 2016.
Defending champions Canterbury Crusaders, NSW Waratahs, Lions, Wellington Hurricanes, Waikato Chiefs and Otago Highlanders are also through to the quarter-finals.
The remaining place rests between Melbourne Rebels, Sharks and ACT Brumbies and will be decided during the final round of regular season matches next weekend.
Waratahs posted a record score as they clinched the Australian conference while Hurricanes beat Auckland Blues to all but ensure a home quarter-final.
Sunwolves were crushed 77-25 in Sydney by Waratahs, who scored 12 tries to three against the under-manned Japanese team, while Hurricanes downed Blues 42-24 in Wellington.
The bonus-point win ended the Canes' three-match losing streak and lifted them five points clear of Chiefs, who retained a faint mathematical chance of hosting a quarter-final when they held off fast-finishing Brumbies to win 24-19.
Jaguares started brilliantly and scored three tries to build a 19-point lead after 20 minutes before Bulls responded with three of their own for a 21-19 half-time advantage.
The Buenos Aires outfit briefly regained the lead through a second try from Gonzalo Bertranou before being run ragged by Bulls.
Jamba Ulengo scored two tries and Marco van Staden one to put the Pretoria team 14 points ahead before Emiliano Boffelli failed to convert after skipper Pablo Matera scored.
TV analyst and Springbok legend Victor Matfield described the match as "fantastic with second-half turnovers giving Bulls the edge".
- Waratahs' biggest score -
It was Bulls' first win in four matches and avenged a 30-point hiding in Argentina two months ago.
Waratahs' biggest score in Super Rugby came after the Sunwolves led 18-12 in the first 30 minutes before the game swung on the red carding of centre Semisi Masirewa for a late lifting tackle on Bernard Foley.
The Tahs led 24-18 at half-time but went on a second-half rampage, adding 53 points to the Sunwolves' seven.
Wallabies full-back Israel Folau returned from his one-match suspension to score a try double, while hulking winger Taqele Naiyaravoro also went over for a brace.
Foley kicked seven conversions and a penalty for 17 points and along the way brought up 900 career points for the Waratahs.
Powerful Ngani Laumape, known as the "Mini Bus" alongside his former All Blacks team-mate Julian "The Bus" Savea, scored four tries as the Hurricanes outscored the Blues six tries to three.
After falling to the Brumbies last week, Hurricanes need to make an emphatic statement to display their play-off credentials and did so in the form of pocket-rocket Laumape.
The 1.71-metre, 103-kilogramme (5ft 7in, 227lb) centre was near unstoppable when he took a head-on approach.
Damian McKenzie orchestrated the Chiefs' win over the Brumbies in Hamilton.
The Brumbies, down 24-5 with 15 minutes to play, provided a storming finish which had the Chiefs rattled, but it was too little, too late.
"I'm proud of the boys, they stayed in there right to the end," relieved Chiefs skipper Charlie Ngatai said.
"We talked about starting strong. We did that, but we were a bit slow in the second."
While the Brumbies made costly errors in the first half, the Chiefs had McKenzie in impeccable form.
In Cape Town, Stormers finished a season in which they suffered a record 10 losses with a morale-boosting win over Sharks thanks to three first-half tries.
Man-of-the-match award winner Cobus Wiese, EW Viljoen and France-bound Raymond Rhule scored to establish a 21-9 half-time advantage for the Cape Town side.
Shark Robert du Preez kicked 11 points to reach 200 for the season and remain the leading scorer, 19 points ahead of Foley.
Marco van Staden and the Bulls brought the Jaguares and Martin Landajo back to earth in Pretoria on Saturday.