The Red Devils, who could not afford to drop another point, lost 1-0 at home to San Lorenzo and went down with one match to go in the 'Final' championship.
With Union already relegated, the third spot for next season in the second-tier Primera B Nacional will go to the wire with Argentinos Juniors or San Martin, who both won on Sunday, the teams in danger.
"We could do no more. When you depend on others [for results] that's that," said rugged defender Cristian Tula after San Lorenzo's victory with a goal by striker Angel Correa.
Relegation in Argentina has been determined since the early 1980s by teams' average points over three seasons with the bottom three in that table going down.
Like River Plate, Independiente were victims not so much of a poor 2012/13 campaign as mismanagement on and off the pitch over at least the past three seasons.
In contrast, they are in 12th place in the "Final", the second of two championships in the season, with a run-in that lifted fans' hopes as they had picked up 12 points from their last nine matches, although only two from the last four.
San Martin are seventh in the 'Final' table but in danger of relegation after only two seasons in the top flight which shows how hard it is for teams to keep their status.
REGIONAL RECORD
Independiente won the Libertadores Cup, the region's elite club tournament, seven times between 1964 and 1984, lifting the Intercontinental Cup, precursor to the Club World Cup, twice.
But the glory days are a distant memory and Argentine FA president Julio Grondona, who was Independiente chairman before taking the AFA post in 1979, feared the worst after last weekend's 2-1 defeat at River Plate.
"This is a big blow but football's like that, it happened to River too," Grondona said after Boca Juniors were left as the only team never to be relegated from the top flight.
In the last 20 years, Independiente have managed only two league titles, boosting their domestic tally to 14 as the third most successful club after River (33) and Boca Juniors (24) in the professional era that began in 1931.
Now they must prepare for the tough second-tier from which River re-emerged as champions at the first attempt.
Former leading Independiente players such as ex-Napoli and Argentina striker Daniel Bertoni say the club must urgently take on a coach and players capable of handling the very different conditions in the Primera B Nacional.
