Gillingham's Cody McDonald hit a late goal to deny
Mark Cooper victory in his first game as permanent Swindon boss.
The hosts went ahead when Nathan Byrne bundled home Nathan Thompson's drilled cross but Danny Kedwell headed in a Chris Whelpdale long throw to equalise.
The Robins retook the lead midway through the second half when Thompson nodded home Ryan Harley's cross.
But Gillingham stole a point when McDonald beat the last man and slotted past goalkeeper Wes Foderingham.
Swindon Town manager Mark Cooper told BBC Wiltshire:
"I thought we deserved to win the game. We played some really good football again [but] you have to see the game out - they have to learn that.
"Our football was really good, the goals were really good and our play deserved more than one point.
"But we didn't see it out and got caught by the sucker punch."
Gillingham manager Martin Allen told BBC Radio Kent:
"It was a good team performance, you've got to give so much credit and praise to the players.
"There's been a step-up in terms of quality in the teams we're playing against. A lot of our players, including myself, have been in Division One, I've been successful in Division One.
"These players can play in Division One, they can stand their ground but it takes a while to get that belief."
Swindon Town 01 Foderingham 02 Thompson 05 Hall 14 McEveley 22 Ward 03 Byrne (Mason - 66' ) 04 Luongo 07 Harley 11 Pritchard 15 Kasim 09 Ranger Substitutes 25 Belford 21 Smith 23 Barthram 41 Archibald-Henville 08 Mason 19 Thompson 20 Storey Gillingham 01 Nelson 03 Martin 06 Legge 23 Harriman 26 Barrett 07 Whelpdale (Dack - 62' ) 11 Weston (German - 75' ) 12 Gregory Booked 18 Lee 08 Akinfenwa (McDonald - 72' ) 09 Kedwell Substitutes 22 Howard 05 Davies 14 Allen 15 Dack 24 Grant 10 McDonald 16 German