3,146 fans were at Old Trafford to see the third round encounter with James Weir, Nicholas Ioannou and Donald Love scoring in normal time but Cameron Howieson's first-half header and a brace by Gilchrist forced the additional 30 minutes.
Paul McGuinness' side took time to get into their stride on the big pitch despite some intricate passing and Adnan Januzaj showing off some clever flicks. The Clarets certainly did not look overawed by the big occasion and Pierluigi Gollini had to be alert to save at the feet of Gilchrist.
The visiting fans were unhappy when play continued with Nathan Lowe lying injured after miskicking a pass but Donald Love's shot was blocked as the Reds pressed on. A promising one-two between Januzaj and Jack Barmby led to James Wilson floating a curler into Callum Jakovlevs' arms and Barmby headed a Love centre onto the top of the net but the deadlock was soon broken at the other end.
Love conceded a free-kick on the left that was played into the near post by fit-again Lowe for captain Howieson to bury a close-range header. The goal was certainly not in the script and the Reds took time to regain their composure with plenty of passes being overhit and going awry.
Willowy midfielder Januzaj continued to provide a creative spark but an electrifying run only brought a corner and it was his smart backheel that led to the equaliser in first-half stoppage time. Weir fed Mats Daehli and continued his run as the ball was moved on to Januzaj to pick out the marauding midfielder and Weir supplied a tidy finish past Jakovlevs.