Play was halted for 27 minutes in the first half after a downpour had left the Glanford Park pitch waterlogged.
Referee Andy Haines took the players off the field while groundstaff worked hard to get rid of the water.
By then Scunthorpe had recovered from a nightmare start to lead 2-1.
Striker Luke Norris fired Gillingham ahead in the second minute after the home defence had been caught napping.
Teenage winger Hakeeb Adelukan equalised for Scunthorpe in the 11th minute, turning his marker in the box to thunder a right-foot shot past goalkeeper Glenn Morris.
Gary McSheffrey then put Scunthorpe in front in the 19th minute – his second goal in successive games – as he finished well after being put through by Paddy Madden.
When play restarted, Madden almost made it 3-1 but was denied by a point-blank save from Morris.
Early in the second half Adelukan also had a great chance to add to the score when he broke free into the box, but fired wide.
Gillingham worked hard in the second half, but could not find an equaliser.