United, now unbeaten in their last eight games, climbed above the visitors in the table after delivering an assured performance bristling with purpose and attacking intent.
Ash Taylor, the Rovers defender, brought some respectability to the scoreline by firing home in the closing stages, but Nigel Clough's side were well worth the win.
Murphy ensured United seized control of this crucial League One fixture between two teams fighting for their lives towards the foot of the table by turning the ball home beyond Tranmere goalkeeper Owain Fon Williams in the seventh minute.
Ronnie Moore, the Rovers manager, has warned that poor defending threatens to undermine the visitors' prospects of avoiding relegation and those frailties were in evidence again when the former Scotland Under-21 international fired home on the turn after Neill Collins had met Baxter's corner.
Murphy's compatriots Flynn and Stephen McGinn went close soon after as United threatened to overwhelm Rovers.
But Lowe served notice that Moore's team would not go down without a fight when he tested George Long's handling having earlier seen a close-range effort cleared off the goal-line by Harry Maguire.
However, when Baxter and Flynn pounced after the break, Rovers crumbled.
McGinn and Porter, who later drew a superb save from Fon Williams, combined to present Baxter with the opportunity to claim his fourth goal in only five outings before Flynn's powerful finish put the game beyond Rovers' reach although Taylor reduced the deficit late in the game.