The four-times world champions had already clinched a playoff spot by finishing second behind group winners Spain, but, after a humiliating 1-1 draw at home to Macedonia on Friday, they were under pressure to perform in Albania.
Italy squandered several good chances until Candreva, unmarked to the left side of goalkeeper Etrit Berisha, was found with a ball across the area from Leonardo Spinazzola and fired home a powerful shot to give Italy the victory.
“We played a great game, were united in our play and we brought the victory home," said midfielder Lorenzo Insigne. "Today we sought the victory at all costs and we managed to win. We gave everything and showed that Italy never gives up”.
Struggling Italy face a two-legged playoff against one of the other eight best runners-up from the European qualifying campaign to secure a place at next year's finals in Russia.
Under-fire Italy coach Gian Piero Ventura told reporters: "In the November playoffs, I hope they (the team) are in better health, I hope we can get back some of the (injured)players.”
Third-placed Albania were eager to show they had improved over the last few years thanks to coaching from Italians. Their current manager Christian Panucci, a former Italy international, spurred his side to attack against his compatriots.
Visiting keeper Gianluigi Buffon kept out a powerful Eros Grezda shot from outside the area before the goal and Panucci was pleased with his side's performance if not the result.
"I am very sorry for the boys. We played as equals with Italy, and Buffon saved more than Berisha. But they punished us just in one moment when we were not attentive,” Panucci said.
It was the first time Italy had played in Albania, across the Adriatic Sea, where they displayed the four World Cup trophies they have won, to the delight of fans who had followed Italian soccer since they were isolated under Communism.
Buffon's shirt was in demand at the end of the game and he exchanged it with striker Armando Sadiku, who said he had asked the keeper for it while they were waiting for a corner.
(Editing by Ken Ferris)
