The Jaguares scored an early try through captain Agustin Creevy when the Blues lost backrower Akira Ioane to the sin-bin for a professional foul.
The Blues also scored when Ioane was absent to make the score 5-5, then led with a try to fullback Matt Duffie, but Blues coach Tana Umaga said his players were to blame for the loss.
"It's up to everyone to understand the plan," Umaga said. "There are key people that need to make those decisions, and I don't believe they did and probably in terms of everyone understanding that plan and just backing it.
"I have got great faith in what we are doing here and not just on the rugby side of it. We know we are underperforming as a whole so that is a challenge and we live for the challenge."
The Reds snapped an embarrassing run of losses by Australian teams to overseas opponents when they upset the Lions to move into third place in the Australian conference standings behind the Rebels and the Waratahs, who lead the table with a game in hand after having the bye.
All four Australian teams were beaten by foreign rivals in last weekend's 10th round, and the 11th round began in similar fashion when the Melbourne Rebels lost 34-18 to the Stormers in Cape Town on Friday then the Brumbies came up short at home to the Crusaders.
The Reds, the Australian team least expected to end the streak after losing its last four games, put a stop to the Lions' mid-season form improvement.
Their first try came after only two minutes to prop Jean-Pierre Smith from a rolling maul and they scored three more, to backrower Caleb Timu, hooker Brandon Paenga-Amosa and veteran flanker George Smith, to lead 24-0 at halftime.
An early second-half penalty made the lead 27-0 and the Reds were well-placed to resist an inevitable Lions rally. The Lions hit back with two tries to Malcolm Marx — his third double of the season — to make the score 27-12 after 62 minutes and added two more tries to Marnus Schoeman.
"I like winning. I'm not much of a participator," Reds coach Brad Thorn said. "But it was never comfortable, no ... 80 minutes is a long time for young men, even my senior guys.
"That's last year's grand finalists, they were always going to work hard to come back."
The Hurricanes remained second in the New Zealand conference standings, a point behind the Crusaders, after thrashing Japan's Sunwolves 43-15 in Wellington, inflating their margin with three tries in the last six minutes, while the Highlanders held on to third spot when Lima Sopoaga booted a long-range penalty after the final siren to secure a 29-28 win over South Africa's Bulls in Pretoria.
- AP