Boca crushed 6-1 by struggling San Martin
The defeat in San Juan prompted Boca manager Carlos Bianchi to apologise and also concede their league aspirations were over.
"To all Boca supporters I say sorry for this defeat they don't deserve," Bianchi wrote in an open letter to Boca fans on Saturday.
"The team and I are ashamed at how we were beaten because this kind of result not only hurts but forces us to rethink many things.
"From now we'll focus our efforts on the Libertadores Cup."
San Martin had gone 16 matches without a victory, while six times South American champions Boca have only one win and eight points after nine matches.
Colombian striker Humberto Osorio, wearing an eye guard that looks like a Lone Ranger mask, put the home side ahead in the second minute and went on to complete a hat-trick with a diving header and a low shot into the bottom corner from a tight angle.
Boca pulled a goal back when 2-0 down with a penalty converted by Uruguayan striker Santiago Silva but hardly had time to dream of a recovery as Landa scored San Martin's third with a fine header into the top corner two minutes later.
The defeat was hardly the best way for Boca to celebrate a century of uninterrupted first division football since their top flight debut on April 13, 1913.
It was Boca's worst defeat since they lost 7-2 at Rosario Central in 2003. The last time Boca were beaten 6-1 in the league was by another San Martin, from Tucuman, in 1988 and they lost 6-0 to Gimnasia La Plata in 1996.
Independiente, the only other Argentine team never to have been relegated, are facing the real possibility of relegation amid threats directed at the players by supporters.
Local media also reported on Saturday that Independiente's trainer Americo Gallego had quit to bring to an end his third spell at the club having steered them to their last league title a decade ago.
Independiente, who conceded a late equaliser in a 1-1 draw at home to Union on Friday night, have 10 matches left in which to try to avoid relegation.
They have taken nine points from nine matches but only 26 from 28 games including the 'Inicial' championship in the first half of the season and remain in the bottom three of the relegation table based on average points over three seasons.
San Lorenzo, whose goalkeeper and captain Pablo Migliore is in prison on charges he perverted the course of justice in a homicide case brought against a Boca hooligan fan, were thumped 4-1 at home by Racing Club.
Unbeaten Lanus opened a five-point lead at the top of the 'Final' championship table with a 2-1 home win over All Boys, who were denied a goal in a controversial offside decision with the score 1-1.
Striker Silvio Romero then drove home a stoppage time winner for Lanus.