Paraguayan former champions Olimpia also reached the last four of South America's elite club competition with a controversial 2-1 victory over Brazil's Fluminense in Asuncion, Uruguayan striker Juan Manuel Silgueiro scoring both goals.
With the aggregate score over two legs locked at 0-0 and no extra time in the competition, Newell's and Boca went into a shootout which began with Boca playmaker Juan Roman Riquelme missing the opening spot-kick.
However, his miss was soon forgotten in an absorbing duel that ended when Newell's goalkeeper Nahuel Guzman stopped Juan Manuel Martinez's effort before winger Maxi Rodriguez converted his to spark wild celebrations at the Marcelo Bielsa stadium.
Boca, who lost their 10th final to Corinthians of Brazil last year, had pinned all their hopes for the season on the competition while languishing near the bottom of the domestic championship.
Newell's, by contrast, are leading the Argentine Clausura standings and now look forward to a semi-final showdown against Brazilian favourites Atletico Mineiro or Mexico's Tijuana, who meet in Belo Horizonte on Thursday with their tie locked at 2-2.
Olimpia, who held Fluminense 0-0 in last week's first leg in Rio de Janiero, go up against Colombia's Independiente Santa Fe in July's semi-finals after the tournament takes a break for the Confederations Cup in Brazil next month.
Newell's coach Gerardo Martino hit out at the poor organisation of the tournament, given that it continues deep into the off-season.
"There are four [Newell's] players whose contracts end [in June]. I don't think it's fair not to be able to count on them [for the semi-finals]," he told reporters.
"Nor do I think it fair that they should not be able to emigrate. This is due to bad organisation of the tournament."
BOCA CHANCE
Boca had a good chance early in the second half but striker Nicolas Blandi's diving header was cleared off the line by defender Milton Casco.
Boca then had Argentina left-back Clemente Rodriguez sent off in the 56th minute for bringing down his namesake Maxi as the winger bore down on goal.
Riquelme was not too generous towards Newell's, claiming they had been lucky to win, forgetting Boca were very fortunate to beat Corinthians in the last 16 when they benefited from some poor refereeing.
"We faced the best team in the country, as everyone says, and we had the clearest chances," he told reporters.
Newell's came closest one minute from the end when Maxi Rodriguez broke through on the right and passed to Paraguay right-back Marcos Caceres, whose deflected shot was somehow turned away by goalkeeper Agustin Orion.
At the Defensores del Chaco in Asuncion, Fluminense took an early lead through midfielder Rhayner, who latched onto a poor backpass by Olimpia defender Julio Cesar Manzur meant for goalkeeper Martin Silva.
Salgueiro equalised with a free kick in the 35th minute, which he told reporters had been meant as a cross but "luckily
