Gretna were unlucky in the early stages when only a tremendous one-handed save by Morton keeper David McGurn kept out Gavin Skelton's fierce drive from ten yards.
And the keeper repeated his heroics seconds later to shut out Paul Murray as he cracked in an angled drive again from ten yards.
But Morton showed they could be dangerous on the break and Brian Graham brought Tony Caig to his knees with a 20-yard effort.
Peter Weatherson had a great chance for Morton just after the break when the ball broke to him ten yards out, but he prodded it well over with his right foot.
Gretna were again unlucky when Kenny Deuchar beat the Morton defenders to a cross from Kyle Naughton, but the ball cannoned back off a post.
Morton kept plugging away and were rewarded on 68 minutes when the ball broke loose in the area and Weatherson cracked it into the corner of the net from 15 yards leaving the keeper helpless.
Just three minutes later it was two as Weatherson again beat Caig after fastening on to a loose ball and cracking it home from 25 yards.
Morton seemed to be denied a penalty on 73 minutes when substitute Iain Russell went down in the box, but was booked by referee Kenny Clark for diving.
However, Morton went three up on 78 minutes when a cross from the right found Chris Millar on the edge of the box, who took the ball under control to shoot home from 15 yards.