United created several openings throughout the 90 minutes but couldn't find a way past an inspired Tatiana Saunders in the Durham Women goal.
And Becky Langley's side were left ruing those missed opportunities when possession was lost just outside their own penalty area, allowing Durham to advance on Claudia Moan's goal, and despite the Magpies shot-stopper keeping out Carly Johns' initial effort, Lambert tapped home into an empty net.
It was United who dominated the opening exchanges and they looked to have raced into an early lead through Deanna Cooper after eight minutes.
Newcastle's number 12 rose highest to meet Demi Stokes' corner but the ball was hacked off the line by Hannah Blake, who stopped a certain goal.
Only four minutes later Amber-Keegan Stobbs latched onto a long ball from Claudia Moan and with Saunders stranded on the edge of her area, the captain could only watch on as her lob drifted narrowly wide.
Saunders came to Durham's rescue seconds later, however, when Amy Andrews' shot was deflected into the path of Shania Hayles who couldn't squeeze her shot underneath Durham's number one.
The away side were posing a threat from set pieces with their best chance of the first half coming in the 26th minute when Johns' attempted overhead kick dropped wide of the far post.
Langley's side proved they're also more than capable from dead-ball situations when Rachel Furness forced Saunders into another stunning save on the half-hour mark, and United couldn't scramble home the rebound.
Despite Newcastle's constant first-half pressure, they were thankful for Moan's heroics as she flung herself in front of a venomous Kalia Novak strike.
Lambert picked out the Canadian at the back post but was thwarted by a stunning point-blank save from United's number 13.
Into the first minute of added time, Saunders once again came to the Blues' rescue. As Stobbs broke into the final third, her long-range effort was tipped onto the bar and behind for a corner.
With just seconds remaining in the first half, United finally got past Saunders who spilt Andrews' cross but Stokes, arriving at the back post, saw her strike cleared off the line by Sarah Wilson.
It took until the 59th minute for the first chance of the second half and it fell United's way. A cross was only half-cleared by Durham, allowing Hayles to swivel and get her shot away, but it was well blocked by Grace Ayre.
The visitors squandered a golden chance just after the hour mark and it was Novak once again. A low cross from Lilly Crosthwaite found the number 17 but her effort was skied well over Moan's crossbar from 12 yards.
Some neat play in the middle eventually saw the ball find its way to Andrews on the left and bearing down on goal against her former club, but she could only fire straight at Saunders from inside the area.
Substitute Beth Lumsden nutmegged Ayre on the edge of the area and decided to go it alone instead of picking out a team-mate, but Saunders stood tall and made a comfortable save with less than ten minutes left to play.
The away side landed a sucker punch to United in the 89th minute as Cooper slipped, and despite an initial save from Moan, Lambert was able to tap home the rebound at the back post.
Newcastle United Women: Claudia Moan, Lois Joel (Emma Kelly 71), Deanna Cooper, Rachel Furness, Demi Stokes, Elysia Boddy, Amber-Keegan Stobbs, Jasmine McQuade, Sophie Haywood (Isabella Sibley 61), Amy Andrews, Shania Hayles (Beth Lumsden 61)
Subs not used: Hannah Hawkins, Liv Watt, Katie Barker, Georgia Gibson, Hannah Greenwood, Charlotte Potts
