Whatever else is wrong with domestic football in Argentina – and it is a lot – it does have the huge advantage of being extremely competitive. Going into the final weekend (although a number of teams are already finished) of the Torneo Inicial, the top four are separated by two points – and are playing each other.

San Lorenzo lead the table by two points and could have wrapped up their first title since 2006-07 in their last match had they not been held to a goalless draw by Estudiantes, their third draw in their last four games. After a break to allow Lanús, one of the other four contenders, to prepare for their Copa Sudamericana final against Ponte Preta, which they won, they now must go to Vélez Sarsfield on Sunday, who won the Inicial last season, and win to be sure of the title.

A draw might be enough, but only if the game in Rosario between Newell's Old Boys, Torneo Final winners last season, and Lanús ends in a draw. If there is a winner between Newell's and Lanús they will play Vélez in a play-off should Vélez win, or San Lorenzo if the game in Liniers is drawn. Vélez will win the title outright if they win and the other game finishes level.

It is San Lorenzo's emergence that is most striking. Lanús and Vélez have, in recent seasons, made themselves into fairly regular contenders for honours by virtue of being run astutely – a rarity in the Argentinian game. Newell's are still benefiting from the sense of purpose instilled by Gerardo Martino, and have in their squad such notable veterans as Gabriel Heinze, David Trezeguet and Maxi Rodríguez. But San Lorenzo have rather crept up on the Argentinian football establishment.

Founded by a priest who, after seeing a boy knocked down by a tram as he chased a ball, felt the need to give the youth of Almagro somewhere to play, they were one of the five original grandes of the Argentinian game. Their success, though, is very much in the past and of their 14 league titles, only three have come since 1974.

In the Apertura in 2011, San Lorenzo finished 17th, lifting themselves away from relegation in the Clausura by coming 12th. Last season, they stabilised and finished 11th in the Inicial before giving the first hints of their progress by coming fourth in the final.

It's not gone unnoticed that since Pope Francis, a San Lorenzo fan, was inaugurated in March, they have lost only six times. He will turn 77 on Tuesday: among those looking for omens it has also not gone unremarked that he might celebrate his first birthday as Pope with a league title.

A lot of the credit must go to the coach, Juan Antonio Pizzi, once a back-up to Ronaldo and Sonny Anderson at Barcelona. His has been a low-key start to management, although he did win the Chilean league with Universidad Católica in 2010.

His success has been rooted in a youthful forward pairing. The 19-year-old Héctor Villalba leads the line in his 4-2-3-1 with the 18-year-old Ángel Correa floating behind him. On the right flank, the 31-year old Leandro Romagnoli, a veteran of the 2001 clausura triumph, chugs up and down, while Ignacio Piatti, signed from Lecce last summer, offers the main goal threat, cutting in from the left. Fans of hilariously awful challenges from players of substantial girth have been disappointed by the way the Paraguay international Néstor Ortigoza has drifted out of the side in recent weeks – he hasn't started a game since the goalless draw at Tigre at the beginning of October – but Enzo Kalinski has done a fine job alongside the 33-year-old Juan Mercier at the back of midfield.

The captain Pablo Alvarado will be missing through suspension, but his central defensive partner Mauro Cetto insisted the mood remains buoyant, despite the recent stutter. "We've got nothing in our heads other than that we'll celebrate on Sunday night," he said. "We're calm. We've had an extra week and we've used the time to decompress a bit. It doesn't seem to me that you have to live a game for 15 days beforehand. The pressure that we feel is normal. If you didn't feel pressure at the moment you wouldn't have blood in your veins."

But while San Lorenzo, if they fail to win, will always be haunted by thoughts of what might have been, Vélez are revelling in suddenly finding themselves in with a chance. As recently as mid-October, they were 12th in the table before a run of five wins and two draws in seven games lifted them into contention, the surge in form at least partly down to the return from injury of the veteran playmaker-cum-left-winger, Federico Insúa.

Vélez will be without Mauro Zarate, suspended after his red card in the 2-0 win over Colón, leaving Lucas Pratto, who has scored in his last two games, to be partnered up front by – probably – Ramiro Cáseres, whose hat-trick against Rosario Central was vital in maintaining Vélez's charge. "We were the last guests to the party," admitted the Vélez defender, Sebastián Domínguez. "We were in a mess but we relied on ourselves. When we've got to this stage, in this manner, we have ended up being a dangerous team."

The title remains San Lorenzo's to lose and as they dread failure, the rest of the country settles back in anticipation of an epic final day and a four-way shootout.