The closely-fought FA Women's National League Division One North affair saw the sides locked level after 74 minutes, before Newcastle's number 11 opened the scoring at Druid Park.
Elson added another in the final knockings to seal the win, bagging her ninth goal of the campaign so far.
After the important victory, which saw Becky Langley's side maintain pressure on league leaders Durham Cestria, the Newcastle Women head coach discussed the impact of her flying left-winger.
"I think Kacie has been on a big journey in terms of her development throughout the last three to four years," Langley told nufc.co.uk.
"I worked with her at Northumbria University and she's flourishing at Newcastle. She's always had that outstanding work-rate and she's always been athletic with great speed, but I think she's really refined the technical details of her game now.
"She's a real threat down that left-hand side when she's cutting in as an inverted winger."
Elson's double helped Newcastle record a sixth win on the bounce, with the Magpies instantly getting back to winning ways following their Vitality Women's FA Cup loss to Wolves Women in December and maintaining their form ever since.
Despite the fillip last weekend's victory gave her side going into the run-in, Langley was quick to reiterate that next week's table-topping clash with Durham Cestria is just like any other game.
"I'm absolutely ecstatic with the win," she said. "I felt like as the game goes into that second half we've always got that extra gear. The overall performance was great.
"It's given us really good momentum going into next week against Cestria. People always talk about how big the game is, and we understand that, but every game is equally important.
"If we hadn't got the job done against Leeds then we wouldn't even be thinking about how crucial the head-to-head against Cestria is."
Newcastle Women host Durham Cestria at Kingston Park Stadium on Tuesday, 14th March at 7.45pm (GMT). Tickets are available now, priced at £3 for adults and £1 for children and concessions. Book yours here.
Photograph courtesy of Colin Lock/@Tyneside_NUWFC
