Durham began the game with a real intensity and had the first chance of note when Andrews pinched possession and squared for Noonan, whose shot was held by Grace Moloney.
But it was the hosts who drew first blood when Nicole Douglas’ shot ricocheted around the area before a cruel deflection took it into the bottom corner.
The Blues’ reaction was good though, and Noonan came agonisingly close to a leveller just three minutes later as she crashed a first-time strike from the edge of the box crashed off the crossbar.
Beth Hepple came closer still moments later, flicking Crosthwaite’s cross over Moloney only to see Lucy Fitzgerald hack the ball off the line.
A deserved leveller would come before long though, as pressure from Andrews saw her chase-down a clearance with Moloney stranded before firing into the empty net.
Hepple then saw a curling strike held by the home stopper as the visitors continued to apply the pressure as half-time approached.
And on the stroke of the interval, Durham thought they should have a spot-kick after Noonan was brought down when through on goal – but their appeals were waved away.
The second half continued in much of the same pattern with the Blues asking more of the questions – Crosthwaite seeing an early cross agonisingly flash past Andrews as she looked to convert.
Lauren Briggs then saw a wicked delivery from the right flank hit the woodwork after a strong spell of pressure.
But with their first real opening of the second half, London City struck – Lindstrom firing home from just inside the area after a rapid counter-attack.
That goal came with just four minutes of normal time remaining, but Durham weren’t deterred and continued to press forward.
And their reward came deep into stoppage time. Hepple’s teasing corner was met by a thumping Robson header at the back post to ensure a deserved point headed back to the North East.