Phoebe Warner scored with just seconds remaining as the Baggies completed a thrilling comeback to claim a 2-1 win in front of watching owner Shilen Patel.
Delphi Cole had fired the visitors in front from the penalty spot after Izzy Green was adjudged to have fouled Evie Priestley.
But substitute Fran Orthodoxou volleyed the hosts level with 17 minutes remaining before Warner fired home from close range, five minutes into stoppage time, to earn the Baggies a second National League Northern Premier win of the season.
The win moved Albion up to fifth in the table, while Wolves sit second after beating Middlesbrough 2-0 for their third victory in a row.
Beth Merrick scored both goals inside the opening 10 minutes and later said the only disappointment was not scoring more.
“We are really proud and happy with the clean sheet and the three points. I think we are a little bit disappointed we only scored two goals,” she said.
“I think we absolutely dominated and it is a bit of a shame it was only 2-0 because the scoreline probably doesn’t reflect the game.”
Wolves trail leaders Burnley on goal difference with the latter having claimed a 2-1 win at Sporting Khalsa.
Claudia Walker and Millie Ravening struck early for the visitors and though Megan Cann pulled one back, the home side could not find a leveller.
Villa boss Natalia Arroyo urged her players to focus on the bigger picture after a 3-1 home defeat to WSL champions Chelsea.
The hosts performed well, particularly in the first half, with Ebony Salmon netting an excellent equaliser after Aggie Beever-Jones had broken the deadlock. Salmon was then denied a second by goalkeeper Hannah Hampton.
But Chelsea’s strength in depth told in the second period, with Sam Kerr scoring in her first appearance for 20 months to seal the win in stoppage time after a Missy Bo Kearns own goal had restored the visiting team’s advantage.
“We were so close to finding the 2-2, until the 92nd, 93rd minute,” said Arroyo.
“I’m so proud of our performance but I know it is about winning and we are not getting anything from this good performance.
“But in the bigger picture, if we keep working and believing as we are doing, we will get bigger things.”
Niamh Deasy scored the only goal as Kidderminster Harriers edged past Stourbridge in a National League Division One Midlands derby clash.
Goals from Amy Rollason, Mia Fellows and Saanya Najib earned Walsall a 3-0 win at Rugby Town in their first West Midlands League match of the season.