The away side enjoyed the lion's share of possession in the opening stages as the Jambos, languishing at the foot of the table, struggled to push out of defence.
David Smith was responsible for kick-starting the home side's first attack just a minute later, however, as he lashed in a cross that was just too long for Sam Nicholson.
Just before the quarter-hour mark, Kevin McHattie's long-range drive was well held by Radoslaw Cierzniak, while a few minutes later, United's Brian Graham handled the ball just before getting a shot in, invalidating his attempt.
Midway through the first half, Dale Carrick skilfully spun away from his marker, before firing in a low shot that Cierzniak just about managed to parry away.
Eventually, the away side drew first blood thanks to an Andrew Robertson cross which fell to Graham, who subsequently fired into the Jambos net from very close range.