All Boys led Lanus 2-0 at halftime at their Malvinas Argentinas ground on Saturday, with two goals from striker Mauro Matos, but ended up losing 3-2 and provoking Falcioni's decision to quit.
Lanus, on a run of five victories, are in a tight bunch of teams challenging for the title in Argentina's "Inicial" championship, first of two in the season, two points behind new leaders San Lorenzo.
Boca Juniors can join the Saints at the top on 30 points from 16 matches if they win at fifth-placed Arsenal later on Sunday while title holders Newell's Old Boys, who have 29, can reclaim the lead by winning at lowly Tigre on Monday.
"After the 3-2 defeat by Lanus, Julio Cesar Falcioni presented his irreversible resignation. The trainer decided to leave the club and told president Roberto Bugallo directly," All Boys said on their website (caallboys.com.ar).
They said reserve team coach Cristian Lovrinsevich would stand in as interim coach for All Boys, who are fighting to avoid relegation at the end of the "Final" championship in May. Relegation is measured in a table of teams' average points over three seasons with All Boys in the bottom three.
Uruguayan striker Santiago "Tank" Silva, who played for the Banfield team Falcioni led to the Apertura title in 2009, scored twice as Lanus came back against All Boys before Lautaro Acosta struck their winner in the 78th minute.
"In the fifth minute (of the second half), when the team had already hit the post, I realised their attitude was different. It was more the merit of the players that what I could have said (at halftime)," said Lanus coach Guillermo Barros Schelotto.
"We went into the match lacking concentration, asleep and lost our way but luckily we managed to turn it round in the second half," he told reporters.
Falcioni also won the Apertura with Boca in 2011 but was never popular with the Bombonera faithful and the club did not renew his contract last year, bringing back record title-winning coach Carlos Bianchi.
Matos is now top of the scorers' list with eight goals with Silva joint second on seven.
San Lorenzo beat Belgrano 4-2 at their Nuevo Gasometro ground in a thriller, going two up in the opening nine minutes before the visitors pulled level after an hour.
Midfielder Ignacio Piatti, in fine form since returning to Argentina from Italy's Lecce last year, restored San Lorenzo's lead with a penalty in the 62nd and former Nantes, Toulouse and Palermo defender Mauro Cetto secured the win with Saints' fourth.
- Sports & Recreation
- Julio Cesar Falcioni
- Mauro Matos
- All Boys