Allan Jenkins scored a 77th-minute equaliser with a strong header after David Cushley had flicked on a Matthew Tipton cross to earn his side a point.
Sean Mackle had headed the Ports into a 55th-minute lead after meeting a cross from Gary Twigg, while Darren Murray headed wide two minutes later.
Defender Ken Oman saw his late header cannon off the bar for the visitors.
Portadown remain seventh in the Premiership table, two points ahead of their opponents at the Showgrounds.
Both sides had a number of scoring chances in the first half but were unable to convert their opportunities.
For United, Gareth Rodger headed over from a Cushley corner, David Miskelly saved a Cushley piledriver with his legs and Jenkins volleyed wide.
Dwayne Nelson saved Twigg's curling effort and also denied Robert Garrett, with Mackle fizzing an attempt wide of the post.
Just before the interval, Twigg found himself in acres of space but rather than shoot, the striker opted to square to Murray, and Rodger raced back to clear.
The match burst into life in the second half and a draw was probably a fair result.