John Paul Kissock, on loan at Gretna from Everton, was on the subs' bench.
With Fabian Yantorno out injured for the remainder of the season, Henry Makinwa partnered Kenny Deuchar up front for David Irons' side.
Makinwa had a shot saved by Morton goalkeeper David McGurn in the eighth minute, but the best chance in the early part of the game fell to Kenny Deuchar.
He got on the end of an Allan Jenkins free-kick and his back-header was only inches wide of McGurn's right-hand post.
Two minutes into the second-half, Morton had a chance to break the deadlock.
A flowing move saw Kevin Finlayson sweep the ball into Peter Weatherson inside the penalty area.
The Ton's top scorer opted to blast the ball with the outside of his right foot, his effort going narrowly wide, when a left-foot strike may have brought a reward.
Weatherson (front) and Chris Millar celebrate Morton's cup win
Morton took the lead in 67 minutes when there appeared to be little danger.
Greacen directed a header into the middle of the Gretna defence, but they were made to pay for their hesitancy by Weatherson, who buried a right-foot shot into the corner of the net.
Three minutes later Gretna were stunned by another Weatherson strike.
The Morton hero worked a one-two with Ryan McGuffie and from almost 30 yards thundered a low shot beyond Caig.
The Morton fans who had travelled to Dumfries were in dreamland when Millar made it 3-0.
Weatherson was involved once more, flicking the ball into the inside-right channel for Ian Russell, who passed to the on-rushing Millar and he dinked it over the Gretna goalie.
Morton now face Queen of the South in the fifth-round of the Scottish Cup at Cappielow on Saturday.
Bookmark with:
What are these?