Juve took the lead after 35 minutes when Di Maria played a perfectly timed pass to Adrien Rabiot, who finished high into the net, with the goal seeming to come as a relief to coach Massimiliano Allegri along with the fans in the stadium.
Di Maria then fed an unmarked Dusan Vlahovic from midfield in the 50th minute, and the Serbian doubled the lead when he calmly beat keeper Joshua Cohen.
The game marked a return to form for Argentine Di Maria, who had struggled with injuries and suspension this season.
"Di Maria was marvellous with his passes, he is an extraordinary player, his first game in quite a while and he did really well," Allegri told Sky Sport Italia.
Juve seemed shocked by the goal and only a great save from Szczesny in the 81st minute prevented the Israeli side from equalising.
"I was very angry at the end because you can't just leave the game in the final 15 minutes and start messing around. You get the chances to score five or six, but if you concede one and then get scared, that is really damaging," Allegri said.
"We tried to be a bit too pretty and then got scared. Let Di Maria do what Di Maria does, let the others focus on what they need to do."
Juve put the game to bed, however, when Di Maria's corner in the 83rd minute was headed by Rabiot into the corner of the net.
Juventus remained third in the group, behind Benfica and Paris Saint-Germain, who drew 1-1 and both have seven points. Juve will meet AC Milan in Serie A on Saturday before travelling to Israel to play Haifa again on Tuesday.