Captain Azeezat Oduntan emerged as the heroine, converting an 89th-minute penalty to send the West Africans into the last four and keep their hopes of a maiden world title alive.
The Flamingos dominated proceedings in the opening half but struggled to make their superiority count, with Oluebube Umejiaku and Oluwakemi Adegbuyi both sending efforts wide of the target.
Akeem Busari’s side continued to press for a breakthrough after the restart, with Kanyinsola Yusuf, Mary Dunstan and Tosin Rafiu also threatening the Venezuelan defence.
Despite enjoying the better share of possession and creating several opportunities, Nigeria appeared destined for a penalty shootout as the contest entered its closing stages.
However, the decisive moment arrived in the 89th minute when Venezuela defender Migleydys Bolsegui was adjudged to have fouled Umejiaku in the penalty area.
Oduntan stepped up and calmly dispatched the resulting spot-kick into the corner of the net to the delight of the players and supporters at the Mohammed VI Football Academy.
Venezuela attempted to mount a late comeback, with Astrid Granadillo and Abril Alejo threatening, but the Flamingos remained resolute throughout seven minutes of added time to secure their place in the semi-finals.
The victory represents another remarkable chapter in Nigeria's campaign, having recovered impressively from a 2-1 defeat to Poland in their opening fixture.
They bounced back with a 2-0 victory over Puerto Rico before defeating defending champions North Korea 3-1 and Mexico 2-1 to reach the quarter-finals.
Nigeria will now face Brazil in Wednesday's semi-final at the Moulay El Hassan Stadium in Rabat.
The South Americans booked their place in the last four after coming from behind to defeat China 2-1 in their quarter-final encounter.
"We gave everything on the pitch tonight. We wanted to keep the ball and play our game, but we made some mistakes," coach Busari said after the match.
"We kept pushing until the end. Reaching the semi-finals is a dream come true for me and a great achievement.
"I'm looking forward to it because I want to make my country proud. We want to give our best in the next match and show everyone what we can do."
