The Italy centre back nodded in Diego's free kick from close range just after the break to give the hosts five points from their opening three games.
Maccabi, bottom of the group on no points, had substitute Tiago Dutra sent off midway through the second half after a studs-up tackle on Chiellini.
The Israeli champions strangely had their best spell after the dismissal with Vladimer Dvalishvili among those to test keeper Gianluigi Buffon but Juve, who have struggled in Serie A for the last month, just hung on.
"What we wanted at all costs today was three points. Winning is the only thing that counts, whether we did it effectively is for others to judge," Buffon told Sky television.
"We conceded a few corners when they were a man down and there was a bit of tension."
Maccabi striker Dvalishvili had also missed a good early chance in the pouring Turin rain when his diving header was expertly palmed away by a full-stretch Buffon.
Juve then increased the tempo but failed to create many clearcut opportunities. Rather than employ his usual two-man attack, Juve coach Ciro Ferrara opted for David Trezeguet as a lone striker in order to make playmaker Diego move closer to the opposition goal.
The change in tactics only worked in patches with Trezeguet flicking a decent chance wide in one good attack.
The French forward was also tugged back by Maccabi centre half Jorge Teixeira but the referee ruled contact was just outside the box amid Juve protests.
Mauro Camoranesi hit the post late on for the home side, whose Brazilian midfielder Felipe Melo was in tears when forced off with an ankle injury.
