Ziaya's superb turn and long-range finish in the 89th minute gave the Algerians a narrow advantage over their opponents from DR Congo on Saturday, ahead of the second leg next weekend.
Ziaya's strike capped a stirring second-half comeback from the hosts, who had appeared set to be the masters of their own downfall at one stage.
After creating a handful of early chances, Mazembe were gifted the lead five minutes after the restart when Said Arroussi turned a left-wing cross into his own net.
But they were hauled level three minutes later, albeit controversially, as Sofiane Younes headed home from close range - with the referee allowing the goal to stand after his assistant had initially signalled for offside.
Both sides continued to create chances from there, with Mazembe spurning several good opportunities to snatch a lead.
However, it was Setif who grabbed a late winner as Ziaya rounded off a fine team move with a clever turn to beat his marker, before firing home from range.