Andrey Finonchenko and Yevgeni Tarasov had put the home side 2-0 up in five first-half minutes but Hen Ezra pulled one back for Haifa and Turgeman levelled the scores in the 78th minute.
The result gave both sides their first point of the group stages after they lost their opening fixtures.
Finonchenko opened the scoring for the Kazakh side in the 40th minute when he headed in Gevorg Ghazaryan's cross from the left.
Tarasov then doubled the lead seconds before the half-time whistle with a close-range strike into the right-hand corner of Bojan Saranov's net.
Ezra hit back early in the second half for Haifa when he drilled the ball into the home side's net but the game seemed to be heading towards a win for Shakhter until Turgeman's brilliant effort drew the sides level.
The former Israel Under-21 international took aim from distance and beat Shakhter goalkeeper Aleksandr Mokin with a sensational dipping drive from 20 yards out.
Shakhter striker Sergey Khizhnichenko had the chance to snatch a late win for his side but he headed his 87th-minute effort over the bar.