Gian Piero Ventura's side were already through to next month's play-offs, but desperately needed a win in Shkoder to be guaranteed the status of top seeds in the draw on October 17th.
"This was the objective we had set. I think we took another small step forward, but we continue to control the game badly and give the ball away too often," said Ventura.
"I had faith when people said the situation was dramatic and I have faith now."
After a tight first half, Inter Milan winger Candreva found the way through after 73 minutes at the Loro Borici Stadium.
Atalanta midfielder Leonardo Spinazzola packed a neat cross from the left for the 30-year-old who rifled into the top of the net from close range to mark his 50th selection for the Azzurri.
"We wanted to prove ourselves after the Macedonia game (1-1)," said Candreva.
"Victories can't be taken for granted. We talked and realised that we had to get back together and be solid going into the play-offs.
"We need the spirit of sacrifice, humility and that Italian character that represents us."
The four-time world champions finished second in Group G behind Spain, who booked their ticket to Russia as group winners, with Italy through to the play-offs on November 9th and 14th as one of the eight best second-placed teams.
Reeling from last month's defeat in Madrid to Spain, Ventura had come under fire after Friday's dire draw with Macedonia in Turin.
And his injury-depleted side were still without stalwarts Andrea Belotti, Daniele De Rossi, Andrea Barzagli, Marco Verratti and Lorenzo Pellegrini.
Italy had a strong call for a penalty turned down in the first half with Ciro Immobile also going close to getting the opener on 21 minutes but Atalanta goalkeeper Etrit Berisha cleared.
Veteran keeper Gianluigi Buffon saved early efforts from Napoli defender Elseid Hysaj and midfielder Eros Grezda.
Italy were denied a penalty appeal before the break when Eder's cross for Immobile hit Empoli defender Frederic Veseli's hand, but the referee waved play on, and again when Insigne was brought down on the edge of the area.
Cristian Panucci's Albania lost their tempo midway through the second half allowing Italy space, with Candreva finding the way through.
Italy now have a month to regain confidence and some of their injured players, although top striker Belotti has already been ruled out of the play-offs.
"I hope to get some players back for the play-offs, as otherwise there might be a problem," conceded Ventura.