Meanwhile, in the 26th minute Tranmere defender Ian Goodison sparked controversy when he caught Kyel Reid in the face with a stray elbow. His actions resulted in a brawl between the two sets of players, but the veteran was only cautioned.
Hosts Bradford came out after the restart with more of a positive intent, but they still struggled to carve out any opportunities of note.
Their failure to do so was punished 21 minutes from time when Lowe sprinted beyond the home defence and drilled the ball into the bottom left-hand corner of McLaughlin's net.
It proved to be the winning moment as the visitors held out over the remaining minutes to collect all three points.