The Lasses took the lead after just seven minutes when Emily Murphy scored her first goal for United.
However, Newcastle were undone through an Aimee Claypoole brace before captain Beth Hepple calmly tucked away a chance on the half-hour mark.
It was United who started the brightest and, in turn, carved open the first chance of the game, which saw them take the lead after seven minutes.
Newcastle looked dangerous out wide, and after recycling the ball on the right, Beth Lumsden's teasing ball into the box allowed Murphy to rise highest and glance her header into the far corner for her first strike in black and white.
The game was very open, and Durham almost got back on level terms when a counter-attack saw Lilly Crosthwaite with no outfield players to beat in Newcastle's half, but goalkeeper Claudia Moan narrowed the angle and forced the shot wide.
A mix-up in midfield then saw Durham pounce and set Mollie Lambert away down the right and send a cross to the back post for Claypoole to head past Moan.
Less than two minutes later, Durham took the lead when Lambert intercepted Charlotte Wardlaw's pass on the edge of the area before sliding in Claypoole, who fired into the bottom corner from close range.
Durham took a two-goal lead on the half-hour mark when Hepple capitalised on a loose Lia Cataldo header in the box before chopping onto her left and bending one into the bottom corner.
United came within the width of the post of pulling one back when Deanna Cooper met Cataldo's deep ball to the back post in first-half added time, but her looping header bounced off the foot of a post and away to safety.
Becky Langley's side began the second half as they did the opening exchanges by dominating the ball and pressing forward, although Lois Joel's low effort on the half-turn rolled wide of the near post.
Just before the hour mark, United were presented with a golden opportunity to get back in the game when Murphy faked to shoot before slipping in Lumsden, but Newcastle's number 26 could only slice her strike down the throat of Rylee Foster.
It was United again who were creating the chances; this time some neat one-touch passing released Amy Andrews down the right, and her fizzed effort landed at the feet of Lumsden, but her thunderous half-volley was well held by Foster.
With just over ten minutes to play, Shania Hayles found herself on the end of a Rachel Furness knockdown in the six-yard box but couldn't keep her effort below the crossbar.
Newcastle United Women: Claudia Moan, Lia Cataldo, Deanna Cooper, Charlotte Wardlaw, Demi Stokes, Amber-Keegan Stobbs (c) (Rachel Furness 46), Hannah Greenwood (Shania Hayles 66), Lois Joel (Jasmine McQuade 66), Beth Lumsden, Emily Murphy, Freya Gregory (Amy Andrews 74)
Subs not used: Grace Donnelly, Hannah Hawkins, Katie Barker, Isabella Sibley, Ava Chapman