Andrews may have been the main attraction but it was one of Raith's less celebrated acquisitions, Paul Currie, a recent signing from Musselburgh Athletic, who caught the eye early on, his precise pass after five minutes setting up a chance for Armand One, who saw his shot saved by Morton keeper David McGurn.
Andrews moved forward in the 13th minute to connect with a Kevin Fotheringham corner but his effort was cleared by the Morton defence.
With regular striker Paul McManus playing wide on the left Rovers appeared to have a wealth of attacking options at their disposal and McManus brought out a superb save from McGurn after 29 minutes with a firmly struck shot from 20 yards.
Raith took the lead a minute later and again McManus was involved, the midfielder's pass reaching One who, despite having his back to goal, swivelled round before stabbing the ball past the helpless McGurn.
Morton rarely threatened in a one sided first half but they almost equalised right on the half time whistle when Peter Weatherson's free kick was blocked by Michael Brown in the Raith goal.
Morton came close early in the second half when substitute Kevin Finlayson tested Brown but Raith should have increased their lead shortly afterwards when a McManus effort struck the crossbar.
A long overdue home win looked to be on the cards for the Fifers at this stage but Morton equalised in the 67th minute when Scott McLaughlin rifled home from the edge of the box.
Ton took the lead five minutes later, Derek Lilley driving home from the penalty spot after Scott Bannerman had fouled Chris Templeman and Templeman himself made it 3-1 with a long range effort in the final minute.