De Zeeuw rose at the far post to head in a free kick on the left in the 57th minute from Paul Merson.
It was a rare highlight in a match of few chances and little excitement for Fratton Park's biggest crowd of the season.
Gillingham, masterminded by player-manager Andy Hessenthaler, gave Portsmouth little room to show the sort of form which has taken them to the brink of the Premiership.
Pompey did not force a corner until the second half and, apart form De Zeeuw's goal, struggled to trouble Gills goalkeeper Jason Brown.
Gillingham striker Paul Shaw twice forced Shaka Hislop in to saves from long distance and Rod Wallace hooked a shot narrowly wide with Hislop beaten on the hour.
Portsmouth Harry Redknapp said after the game: "You're going to get games like that and I have to admit we were hanging on a bit at the end.
"But Gillingham are a difficult side to beat and we are never going to batter every team we meet.
"In the end it is three more points and with 13 matches to go we are in a tremendous position, 12 points clear of the team in third place."
Hessenthaler said: "I am not sure we deserved to lose. We limited Portsmouth to a couple of half chances and we might even have nicked an equaliser in the last few minutes.
"It showed how much progress we have made this season, beating Leicester and running Portsmouth so close.
"Portsmouth and Leicester are the best two teams in the league and they will go up without a doubt."