Josh Stones put National League York ahead in the Yorkshire derby at Oakwell but two Davis Keillor-Dunn goals turned the tie on its head.
Mark Kitching looked to have sent it to extra time but a stoppage-time header from Marc Roberts has spared Barnsley's blushed against a side ranked 44 places lower than them.
GOAL: Reading 2-2 Carlisle Unitedpublished at 16:57 GMT 1 November
16:57 GMT 1 November
Regan Linney (90+8 mins)
Can you believe it?! Carlisle are level in the EIGHTH minute of additional time!
Their hard work and endeavour has meant they have stayed in the game throughout and more good work from Chris Conn-Clarke sees him find his former Altrincham teammate Regan Linney who finds the bottom corner with his right foot.
Incredible - they were 2-0 down five minutes ago and now they're taking the match to extra-time! And Linney has them both!
Both sides have their keepers to thank as we head closer and closer to extra time. Jordan Wright saved well from Sam Gale and, before that, a mix of Jake Turner and the woodwork denied Kai Whitmore.
There were 11 minutes of time added on after that stoppage and we're half-way through. Tense.
Four-time FA Cup winners Bolton see off Huddersfield in this all League One affair.
Ibrahim Cissoko put the Trotters ahead before Bojan Radulovic equalised for the Terriers but Richard Taylor's goal in the 69th minute sees Steven Schumacher's side through.