Siriki Dembele was brought down by Callum Brittain just outside the area and Brannagan drove the 67th-minute free-kick high into the far corner of the net with goalkeeper Aynsley Pears helpless.
It remained 1-1 until full-time, although Argyle goalkeeper Dan Grimshaw, back in the team after an injury to Conor Hazard, made two good stoppage time saves from Oxford substitute Siriki Dembele.