The visitors declared their first innings on 150-1 before the start of play with the captains eyeing a result.
Harry Finch (74 not out) and Luke Wells (44 not out) scored quickly as Sussex declared on 142-1, a lead of 320.
Gloucestershire were toiling at 88-5 but Taylor (69 not out) and Noema-Barnett (37 not out) saw out the match.
They finished some 109 runs short of the winning line, on 212-6, to deny Sussex fourth win in five County Championship games.
Visiting opener Cameron Bancroft took his maiden first-class wicket in a Sussex innings which was all about building runs for a chase, but a result did not materialise.
An unbeaten 95-run partnership between Jack Taylor and Kieran Noema-Barnett guided Gloucestershire to a draw against Sussex at Hove in Division Two.