Hapoel had little to offer as Dinamo raced to a 2-0 lead with goals by Izet Hajrovic and Mislav Orsic in the half hour.
Arijan Ardemi added a second-half brace and a late strike by Armin Hodzic effectively sealed the tie.
It was a dreadful debut for Hapoel's Greek goalkeeper Giannis Anestis, who was at fault for all five goals but Israeli manager Barak Bakhar refused to blame his new signing.
"This was a weak team performance and we showed no character. It creates a small crisis but this team has overcome bigger ones."