The Clarets earned another home tie against Leicester City in the fourth round after grabbing two late goals against a strong Forest side.
The game opened with both teams trying to gain an early goal.
A long-distance cross passed wide of the Clarets goal and in reply Evie Priestley shot wide of the Forest goal as the game swung from end to end.
Sarah Greenhalgh struck a couple of long-distance shots, but nothing to trouble the Forest keeper.
Forest won possession from a Burnley clearance and crossed for centre forward Ellie Casper close to the penalty spot.
Her swing at the ball was swiftly blocked by Olivia Wilson in the centre of the Clarets defence.
Burnley pressed forward, and the Forest keeper had to collect several crosses into the box.
The final 10 minutes of the half produced a few chances. First a long run into the Clarets half by Bolu Fisher, followed by a curling shot, had Lauren Bracewell beaten, but the ball hit the angle and was cleared, to the relief of the home side.
The visitors maintained the pressure, with Burnley having to defend a free kick, and then Bracewell intercepted a through ball.
The Clarets came close to snatching a goal when Evie Priestley was on hand to collect a bungled clearance from a Sarah Agger cross.
Priestley shot at goal, but the visiting keeper made a great diving save.
Nottingham Forest finished the half strongly. Bracewell ended a goal mouth scramble by diving and smothering the ball, and was soon back in action as she attempted to tip over a close range shot that hit the crossbar.
The Clarets had a penalty shout waved away when Priestley appeared to be pushed over in the box, but the final effort resulted from the league’s top scorer Precious Hamilton, breaking forward at speed and shooting, forcing Bracewell into an excellent diving save.
All in all, the Clarets were relieved to be going in at half time with the score line level.
As the second half got underway, Forest seemed content to maintain possession but struggled to create clear chances for quite some time.
After 15 minutes, a long ball floated into the Clarets box and was met by Fisher, who failed to connect cleanly and Bracewell collected.
Fisher’s efforts were rewarded shortly afterwards when Forest mounted a concerted attack, and Hamilton threaded a pass back from the bye line to Fisher, who shot home to open the scoring.
In reply, a Lizzy Hamer effort was blocked in the box, before another attack by Forest saw Hamilton work through the Clarets defence and shoot from 18 yards, but the ball passed wide of Bracewell’s post.
Kelly Halligan had a shot saved neatly by the Forest keeper, and soon the Clarets were attacking again. A Lizzy Hamer pulll back from the bye line picked out Sarah Agger on the wing. She shot superbly from 25 yards, catching the keeper off her line, and the ball dropped under the cross bar to make it 1-1.
The Clarets were quickly back under pressure, and Mel Brown made a well-timed tackle in the box to prevent a Forest striker running in on goal, but the Burnley side had new determination and were consistently pressing forward and causing problems.
A Forest defender was booked for pulling Greenhalgh back as she was breaking through, then a foul on Hamer resulted in a free kick close to the touch line, level with the penalty spot. Nic Worthington stepped up to the kick and drilled the ball low and hard into the crowded box. The ball took a slight deflection off a defender before hitting the back post and finding the net.
With several minutes to play Burnley had to dig deep and defend hard, which they did successfully until the final whistle.
Up next, Burnley FC Women are back in league action on Sunday, when they travel to Derby County LFC, at Mickleover Sports Club, Station Road, Mickleover, Derbyshire, DE3 9FL. Kick-off is 2 p.m.