The Vixens slowly clawed their way back in to the contest and were down by only one goal with a minute left; they squared the ledger with 30 seconds remaining before Tegan Caldwell took three attempts to drain the winner with 17 seconds left on the clock.
The Magic had the final possession of the game but were unable to get the ball in to Irene van Dyk to find an equalising goal and were forced to leave Melbourne empty handed.
Vixens wing attack Madison Browne, who produced a game-high 15 goal assists, said the home crowd got them over the line.
"I don't think it was our best netball on court today," she said after the game. "But credit to the girls, we fought it out right until the last minute. I think we gave everyone a heart attack but [it's] great to get the win."
Statistically, the Vixens shot the ball better, with Kate Beveridge proving tough to contain as she made 18 of her 23 attempts on goal, while Caldwell was resolute as she made 17 from 21.
Magic goal attack Julianna Naoupu struggled in the first half as she only made nine from 17 and was replaced for the final two quarters by Jess Waitapu who made five from seven, while van Dyk registered 25 goals from 30 attempts.
Langman was busy throughout the game as she claimed three of the Magic's nine intercepts - Melbourne only grabbed one - and added 10 goal assists as she fed the shooters with great direction.
Vixens goal keep Geva Mentor had a strong game as the Australian international tussled with van Dyk, while Magic defenders de Bruin and Williams each made two steals.
The Magic have plenty of time to think about their next game as they don't host the Canterbury Tactix until Monday, April 30 in Rotorua, while the table-topping Vixens meet Queensland in Melbourne next Sunday.
In the other Sunday afternoon fixture, the NSW Swifts beat the Queensland Firebirds 54-49 in Sydney.
Melbourne Vixens 40 (Kate Beveridge 18/23, Tegan Caldwell 17/21, Karyn Howarth 5/7) Waikato-BOP Magic 39 (Irene van Dyk 25/30, Julianna Naoupu 9/17 Jess Waitapu 5/7) 1Q: 10-11 HT: 20-22 3Q: 29-32
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