However, it was Town who struck the first blow with just three minutes played, as Neil Ashton swung in a left-foot free-kick from the right and Stewart Drummond arrived on cue to head home towards the far post.
Walker drew the Pirates level with 21 minutes on the clock, expertly touching the ball home at the near post after Ryan Green had reached the byline and cut the ball back.
Ten minutes before the interval Rovers hit the front, as a long ball forward through the left channel caught out the Shrews defence and Walker strode on to lift a superb chip over the advancing Chris MacKenzie.
After the interval Town pushed forward hoping to find an equaliser, but they struggled to break down a stubborn Rovers backline, with Steve Elliott an inspirational figure.
With just over ten minutes to play, the Shrews almost grabbed a lifeline when Derek Asamoah met Marc Tierney's cross from the left, but keeper Steve Phillips made an instinctive close-range block.
Tierney then managed to get himself booked twice in the space of four minutes and was dismissed, before Rovers wrapped up victory in stoppage time.
Every Town player was up for a corner and when the ball was cleared, Sammy Igoe raced clear to roll the ball into the empty net from 35 yards.