The hosts took the lead in the first half through Leon Legge despite appeals for offside amid claims the ball brushed a Gillingham player's head, which resulted in a flag from the assistant - subsequently overruled by Williamson.
Dagenham battled back and at the second time of asking, Femi Ilesanmi hammered his side level soon after the break.
But three minutes after coming off the bench, Deon Burton tucked home his 11th goal of the season after Daggers keeper Chris Lewington was adjudged to have brought down Anton Robinson - another decision Still disagreed with.
With Port Vale losing at home to Morecambe, Gillingham went top of the table for the first time since January and in doing so put their last home match - a 1-0 defeat to Wycombe - to bed.
"It was defending at its best, everyone to a man stood firm, stood their ground and reduced them to very few chances," said Gills boss Martin Allen.
"When they got the equaliser we all know what could have happened but our players responded very well, they stepped up another gear.
"We decided to go with all-out pace with Cody and Myles, who were both fantastic and God bless Deon coming on I thought he was great, the substitutions worked really well out there.
"The real test when you're manager is when you don't play well and you get a defeat and it's not very good. That's the real test as a manager.
"That Wycombe game, it's my job and I've got to stand up in front of those players and deliver. I have to bring them back up and give them a game plan. Until we get the job done, I don't drift off into fantasy island, but it would be lovely to stay top."