Mauro Camoranesi scored what proved to be the winner in first-half stoppage time when his shot deflected off Haifa defender Dekel Keinan to beat goalkeeper Nir Davidovich.
Second-placed Juventus have eight points behind Girondins Bordeaux, who have qualified on 10 points after their 2-0 win at Bayern Munich. The German side are third on four points.
"I am pleased that we won, the players played thoughtfully and responsibly, it wasn't only a case of them using their feet," Juve coach Ciro Ferrara said through a translator.
"Our disappointment at drawing at home to Bordeaux has passed. We now look forward with the hope that we can qualify for the knockout phase," he added.
Juve drew their first group game 1-1 with Bordeaux, who reached the knockout round with a 2-0 win at Bayern Munich. Juve visit the French champions in their next match on November 25.
WEAKEST PERFORMANCE
Haifa coach Elisha Levy said his team's first-half performance was their weakest in the competition so far.
"Naturally, we're very disappointed. Clearly, in the first half we didn't play as well as in our other games. Juve pegged us back and did not allow us to do the things we wanted to do. It was much better in the second half for us," Levy added.
