Led once again by in-form striker Danny Carlton the Shrimps extended their unbeaten run to seven games to hold on to fifth spot with just one game to go.
The deadlock was broken by Wayne Curtis on 14 minutes. Michael Howard floated a free-kick into the penalty area, Jim Bentley flicked on and Curtis was in the right place at the right time to volley home the loose ball from close range.
That was the spark Morecambe needed to step up the pace as they created a string of first-half chances.
In the space of five minutes a Gary Thompson cross flashed across the goal, Fraser McLachlan saw a shot deflected just wide of the right hand post and Curtis came close to adding a quick second.
McLachlan was again close to his first Morecambe goal with a fierce volley which cannoned back off the underside of the crossbar before the Shrimps added a well crafted second when Carlton scored his eighth goal in the last seven games from close range.
The pressure continued in the second half with Carlton adding another to his tally just 31 seconds after the break. The striker raced on to Curtis' long throughball, rounded keeper Craig Holloway and slotted the ball into the empty net.
Carlton thought he had clinched a superb hat-trick but saw a third strike chalked off for offside, before Ged Brannan almost scored with a wonderful volley which came back off the underside of the woodwork.
Gravesend were second best all the way through and produced just one shot on goal - an 85th-minute volley from Bradley Johnson which forced Steven Drench into a neat save.