The Shrimps stormed into a 3-0 lead inside the opening 32 minutes, but they did not have to work too hard for their goals with Exeter's defence all over the place.
Andrew Fleming swept in the first from 18 yards when Craig Woodman's poor pass across his own box fell at the midfielder's feet, and the next two goals were the result of mistakes by Exeter goalkeeper Artur Krysiak.
He raced from his goal to deal with a long ball only to hand it straight to Fleming and he lobbed into a vacant goal from 30 yards. Then Izak Reid capitalised on some hesitancy on the edge of the box by Krysiak to again lob the hapless Pole.
Exeter were frustrated when Alan Gow scored midway through the second half, but the referee had already blown for a free-kick. The Grecians had plenty of possession, but could not find a way past Barry Roche in the Morecambe goal.