Nicolas Otamendi and Rafa Silva also scored in the first half and Benfica never looked troubled in making Thursday's draw as they qualified for the 12th time in 13 seasons.
Neres set up the first goal as his deep cross picked out Otamendi, who drifted away from his marker and headed home.
Silva profited from a defensive mistake as he intercepted Oleksandr Syrota's wayward pass and produced a neat finish.
Goncalo Ramos then picked out Neres, who brilliantly bent the ball into the net to wrap up the scoring for the home side.
The defeat is a bitter disappointment for Dynamo, who could not book their passage on the day league football returned to war-torn Ukraine.
Aleksandar Pesic and Mirko Ivanic had put the Serbian side ahead in the tie but it was in the balance again when Daniel Sundgren pulled a goal back for Haifa just before half-time.
It looked headed for extra time until the unfortunate Pavkov turned the ball into his own net in the 90th minute. It is the first time Haifa have reached the group stage since 2009.
Czech outfit Plzen also booked a place in the lucrative group stage as they came from behind to beat visitors Qarabag 2-1 and win the tie by the same score on aggregate.