Eighteen Torino players and officials were among 31 people killed in the accident on May 4, 1949, when their plane crashed into the Superga hill near Turin.
The 'Grande Torino' team, returning from a match against Benfica in Lisbon, had won the Serie A title five seasons in a row but won it just once after the crash, in 1976. Juve meanwhile have racked up 35 titles and recently secured their eighth in a row.
Torino beat Milan for first time since 2001 as Mertens equals Maradona
Now they are closing in on the Champions League after a fine season that culminated last weekend with their first win over AC Milan since 2001, which put them just three points from the top four.
"We mustn't think about the Champions League, what we need to do is to keep cool and keep our feet on the ground," said Torino president Urbano Cairo after the win.
"In this final rush it is very important to be consistent. We now have to think about next Friday and an extremely important game against Juventus.
"The race for Europe is still wide open, but I saw a very determined Torino."
Torino have not won at Juventus since 1995 with their only win since then against their city rivals at home in April 2015.
Juventus have already wrapped up the title but their hopes of equalling their points record of 102 from the 2014 season were ended after last weekend's 1-1 draw against Inter Milan.
But they can still achieve a century if they win their remaining four games, with Portuguese superstar Cristiano Ronaldo targeting the top Serie A scorer crown, with 20 league goals so far, three behind Sampdoria's Fabio Quagliarella.
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Torino captain Andrea Belotti is back to his goalscoring best, with six goals in eight games and 13 for the season, including the opener against AC Milan.
Should they make the top four it would be their first appearance in Europe's top club competition since 1976-77, when they were knocked out of the old European Cup in the second round.
Behind Juventus and second-placed Napoli, who host Cagliari on Sunday, the battle for elite European football remains tight with six teams in the running.
Juventus could play a role in who goes through to next season's Champions League as after Torino they play Roma the following weekend and Atalanta on May 19.
Atalanta, are fourth, with 59 points from 34 games, one point ahead of Roma, who are fifth.
The side from Bergamo are on a nine-game unbeaten run in Serie A and head to Lazio on Sunday ahead of the Coppa Italia final in the Stadio Olimpico on May 15.
Inter Milan, on 62 points, are three points ahead of Atalanta, and can consolidate third place at struggling Udinese.
Roma, meanwhile, travel to Genoa looking to extend their unbeaten run to six games and return to the Champions League places.
Gennaro Gattuso's Milan host Bologna on Monday having slipped out of the European berths into seventh, with just five points from their last seven games.
AC Milan are on level with Torino on 56 points with Lazio still in the running in eighth on 55.
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