Charlie Hughes put Burnham ahead on 26 minutes only for Sam Edwards, making his first start since September, to equalise for 'Side just six minutes later. It was the midfielder's fourth goal of the season.
Gulfer's men got off to a great start after the break as the ever reliable Marvin Birch scored on 50 minutes to put 'Side in the lead. It was the enforcer's third goal of the season and one that looked likely to be the winner as time began to run out.
However a goal deep into stoppage-time from Bradley Morgan for Burnham denied 'Side the win, much to the annoyance of the fans, staff and supporters.
'Side are next in action on Wednesday night when they face Eton Manor away in the Gordon Brasted Memorial Trophy.
‘Side: Jack Francis, Ibrahim Conteh, Fionn Glancy, Paul Wright, Maxwell Amoako, Sam Edwards, Augustus Ruzgas, Marvin Birch, Luke With, David Laird, Jakub Berkowicz.
Subs Not Used: Kieron Walker-Browne, George Ademiluyi