Rodrigo Gomes had given Wolves a first half lead when he followed up on a missed Hwang Hee-chan penalty to finish.
But the visitors quickly fought back to take a 2-1 lead with headers from both Tomas Soucek and Lucas Paqueta.
Wolves looked destined for another defeat until Larsen stepped off the bench and seemingly did not allow the ongoing interest in him from Newcastle United to affect him.
The striker scored twice in two minutes to send Molineux into raptures and secure Wolves’ place in the third round of the Carabao Cup.
Analysis
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Vitor Pereira made eight changes to the Wolves side that lost to Bournemouth last time out.
Among them was Fer Lopez, who made his first competitive start for the club, alongside Yerson Mosquera who made his first appearance since suffering a serious knee injury almost a year ago.
Former Wolves defender Max Kilman was on the bench for West Ham, as Graham Potter named a strong side.
It was a remarkably quiet opening 25 minutes at Molineux, as two sides with poor starts to the season took each other on.
A good Lopez free-kick caused a scramble in the box in the only notable action, until West Ham had a huge chance.
Jean-Clair Todibo (Photo by Shaun Botterill/Getty Images)
Jarrod Bowen set up Soucek, who turned Emmanuel Agbadou and had a shot from 12 yards, but Sam Johnstone got down well to make a fantastic save.
Moments later, the Wolves goalkeeper was called into action again for another good stop to deny Bowen.
Wolves were struggling for any attacking threat and they were failing to use the wings properly.
That was highlighted by one moment where they did look dangerous, as R.Gomes made a strong attacking run down the right and he won a corner after getting to the byline.
Wolves were then awarded a penalty out of nothing when Jean-Ricner Bellegarde was brought down by Guido Rodriguez.
Hwang stepped up to take the spot kick and smashed the post, but R.Gomes reacted quickly to squeeze home the rebound beyond Alphonse Areola at the near post, despite the goalkeeper getting a hand to it.
Wolves then took that lead into half-time.
Wolverhampton Wanderers' South Korean striker #11 Hwang Hee-chan (Photo by PAUL ELLIS/AFP via Getty Images)
It only took five minutes of the second half for the Hammers to equalise through Soucek.
Kyle Walker-Peters put in a cross to the far post and the midfielder beat R.Gomes with ease to head home.
Wolves initially reacted well to the goal with some attacking intent, crosses and crunching tackles - one of which resulted in an Agbadou booking.
But that all counted for nothing when some more terrible defending from Wolves allowed the visitors to take the lead in the 63rd minute.
Bowen crossed from the right and Paqueta was left free - between Agbadou and Mosquera - to head home.
Wolves were pushing for an equaliser and finally found it eight minutes from time when Andre had a shot saved and substitute Larsen did well to get a left foot on it and find the roof of the net.
If that was not enough, Larsen then put Wolves back into the lead just two minutes later. Jhon Arias had a shot saved first before Jackson Tchatchoua crossed for Larsen to head home at the near post and send Molineux and the Wolves dugout into raptures.
The Norwegian striker almost scored his hat-trick in added time but he fired over the bar, as Wolves saw out the win and advanced in the Carabao Cup.
Key Moments
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GOAL 43 R.Gomes reacts to a missed penalty to put Wolves ahead
GOAL 50 Soucek levels with a header
GOAL 63 Paqueta heads West Ham into the lead
GOAL 82 Larsen finishes to equalise for Wolves
GOAL 84 Larsen heads home a winner
Teams
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Wolves: Johnstone, R.Gomes (Tchatchoua, 72), Mosquera (Doherty, 72), Agbadou, S.Bueno, H.Bueno, Andre, Bellegarde (J.Gomes, 72), Lopez (Larsen, 72), Arias, Hwang (Kalajdzic, 80).
**Subs not used:** Bentley, Wolfe, Munetsi, Chirewa.
West Ham: Areola, Walker-Peters, Todibo (Wilson, 86), Mavropanos, Aguerd (Kilman, 70), Diouf, Rodriguez (Fullkrug, 86), Ward-Prowse, Soucek, Paqueta, Bowen.
**Subs not used:** Hermansen, Scarles, Potts, Irving, Marshall, Orford.