Friday night's match at GIO Stadium made it 210 minutes since the ACT-based franchise last scored a try.
It is the first time the Brumbies have lost four on the bounce since 2011.
"Six games this year where we've lost by seven points or less," Brumbies coach Stephen Larkham said.
"It's tough and heartbreaking and something that we're obviously embarrassed and disappointed with."
The opening 25 minutes were played almost exclusively in the Brumbies' attacking half.
But after winger James Dargaville had a try disallowed in the opening stages, Wharenui Hawera's 18th-minute penalty goal was all they had to show as they went to the break leading 3-0.
While the Lions managed to get on the front foot a handful of times before the break, it was their defensive guile that allowed them to stay in the fight.
Elton Jantjies levelled the scores 10 minutes after the break, with a penalty goal the first sequence of a game-changing one-two punch.
Brumbies fullback Aidan Toua threw a wild pass, which was pounced on by Lions centre Lionel Mapoe who gave the offload to flanker Kwagga Smith.
The former sevens' star showed an electrifying turn of pace to run more than 60 metres and score the only try of the match.
Jantjies converted to give the visitors a 10-3 lead.
With the game opening up, Lions winger Courtnal Skosan gave away a penalty for not releasing the ball, allowing Hawera an easy shot to shave the deficit to four.
But despite halfback Joe Powell twice breaching the Lions' line, the Brumbies try-scoring hoodoo continued.
An offside penalty in the dying minutes gave Lions fullback Andries Coetzee the chance to put the icing on the cake with the final kick of the match.
The victory cemented the Lions at the top of the South African conference with their seventh-straight win, boosting their record to 10-1.
"It was probably one of the games where we played the least amount of rugby in the last three or four years," Lions coach Johan Ackermann said.
"They put a lot of pressure on us, but we just couldn't get the ball.
"So it obviously makes the win even more special to end the tour like that."
Remarkably, the Brumbies will remain top of the Australian conference at the end of the round, despite a 3-7 record.
The Brumbies face a tough world tour to play South Africa's Kings in Port Elizabeth and Jaguares in Buenos Aires, while the Lions will aim to continue their winning streak in a derby against the Pretoria-based Bulls.