Bradley Dack took advantage of a series of Morecambe mistakes to flash a shot past Barry Roche from six yards out to level the scores in the 52nd minute after Jack Redshaw had given the home side a first-half lead.
Redshaw scored for the fifth time in six games with a close-range finish just before half-time after Stewart Drummond's right-wing cross had been knocked into the box by Gary McDonald.
The visitors went close to taking the full three points when Matt Fish flashed a shot inches over the bar and Dack went close to a second with a flicked header that sailed just wide of a post.
Redshaw went close to giving Morecambe the lead after 18 minutes when he volleyed over after a poor defensive header from Fish.
The diminutive striker also drilled a shot wide after Gillingham's Michael Richardson almost put the ball into his own net when looking to divert a Will Haining cross.
The five bottom sides in League Two are now all separated by goal difference following a day of mixed results for the relegation candidates.
A Lee Molyneux hat-trick gave bottom side Accrington a crucial 3-2 win over fellow strugglers Barnet.
Molyneux put Stanley 3-0 up at half-time before Elliot Johnson and Ross Jenkins gave Barnet hope but they could not find an equaliser, and the late dismissal of player-manager Edgar Davids made the Bees' afternoon even worse.
The result left both sides on 40 points, with Aldershot joining Accrington in the bottom two after Jack Midson scored the only goal to hand Wimbledon the points at the EBB Stadium.
Plymouth also sit on the 40-point mark following a 2-1 home win over 10-man Fleetwood. A Paul Wotton penalty put the hosts 1-0 up with Jason Banton doubling their advantage before the break. David Ball pulled one back for Fleetwood, who had Paul McKenna sent off late on.
Torquay are the fifth and final side on 40 points after coming from behind to take a draw against Southend. Freddy Eastwood opened the scoring for Southend but Joss Labadie levelled in first-half stoppage time to secure a point for Martin Ling's side.
As Gillingham saw their lead cut, Port Vale took advantage of their draw, moving into second place and closing the gap to the leaders courtesy of a 2-0 win at York.
Burton had been second before the day's fixtures but they could only draw 1-1 at Dagenham and Redbridge, and Cheltenham remain fourth after a 3-0 home win over play-off hopefuls Rotherham.
Exeter's 4-1 win over Capital One Cup finalists Bradford means they stay just a point behind Cheltenham in fifth, while a brace from Ellis Harrison secured a 2-1 win for Bristol Rovers at home to Rochdale, who had equalised through Michael Rose before Harrison's late winner.
Marc Richards' fifth-minute goal was enough for Chesterfield to win at Oxford whilst Wycombe's home game with Northampton was postponed due to a waterlogged pitch.