That could be achieved tomorrow when they host Atalanta at the Stadio Friuli knowing a win would be enough to keep Lazio and Roma at a safe distance, should the two Eternal City clubs fail to win.
"Months ago, nobody would have imagined it, but with two games of the season to go, we are right on course for a place in Europe and we want to keep this chance alive right to the very end," said coach Francesco Guidolin.
"My secret is the many youngsters I have in my squad who all want to win."
The other secret is the elder statesman in his side, Antonio Di Natale, who despite missing a penalty against Palermo in midweek, has accounted for 20 of the Zebrette's goals this season.
Di Natale did not even want to take that penalty in midweek and was forced to do so by Guidolin, who subsequently substituted his top goalscorer, who went straight to the dressing room without saluting his coach.
He is a doubt for tomorrow's game, but not because there are hard feelings between the coach and his striker.
"It was a misunderstanding," said Guidolin, who had not recognised that Di Natale did not want to take the penalty due to an injury he has been carrying in recent weeks.
Opponents Atalanta secured their place in Serie A in midweek, but striker German Denis is not satisfied with his own season.
"I could have scored more goals," he told tuttoatalanta.com. "I just lacked some consistency in that area.
"We knew it was going to be a hard season but we showed that we deserved to stay up.
"We have lacked attention at times, but that is the only criticism that can be levelled at us."