Ortiz netted in the 55th minute following a goalkeeping error from Stas Pokatilov as unbeaten AZ moved six points clear of third-placed Maccabi Haifa with two games in Group L remaining.
Shakhter, who held the Dutch side to a 1-1 draw in the reverse fixture, were poor throughout after breaking the record for the longest journey in the history of UEFA group stage football.
They were only able to name three substitutes against AZ, who made a bright start to proceedings, with Roy Beerens' strike from the edge of the area blocked by Shakhter midfielder Serhiy Maliy.
Mattias Johansson then saw his shot from just outside the box caught by visiting goalkeeper Pokatilov.
Chances were few and far between as the half wore on although Pokatilov was kept on his toes after being forced to tip away another long range effort from the lively Beerens, with Jan Wuytens heading wide from the resulting corner.
Beerens tried his luck again from distance but was once more thwarted by Pokatilov shortly after half-time before AZ were rewarded for their attacking persistence, albeit following an error from Pokatilov.
The Shakhter number one allowed Ortiz's angled drive at his near post to slip through his hands 10 minutes after the break.
It was unfortunate on Pokatilov, who had been faultless up until that point.
Shakhter could not find a way through the AZ defence although Maksat Baizhanov's shot 13 minutes from time that missed the target did at least give the away fans some hope their side could find a leveller in the closing stages.
While it was AZ who finished the stronger side, Roger Canas nearly rescued an undeserved point for the Kazakhstan champions but shot wide from just outside the box.