It would have filtered through to both sets of players as to how important a victory was to respective sets of supporters, although it was Gillingham who seemed more intent on gaining victory in the first half after creating a number of chances in the opening 10 minutes.
Danny Spiller sent a deflected header over the bar, Darren Byfield's dipping shot landed just over and Spiller then again went close from 12 yards as Rhys Evans parried at full stretch.
Swindon then posed a threat when Rory Fallon flicked on to Charlie Comyn-Platt whose header was well held by Jason Brown.
Gillingham then came surging forward again when Spiller threaded the ball through to Micheal Flynn and his first-time shot under pressure was kept out by Evans' legs.
Gillingham's pressure paid off though with the opening goal on 20 minutes.
Alan Pouton's shot from outside the box looped up into the air and Byfield rose above Evans to head home.
The scoreline stayed that way for the remainder of the half and then Swindon came close to equalising on 52 minutes, but Brown blocked superbly from Fallon's back post header.
Gillingham then added a second when Spiller embarrassed Aaron Brown on the right before pulling the ball back for Flynn to finish.
Gillingham made absolutely sure of the points when neil Harris bundled the ball over the line to wrap up a comprehensive victory for the Kent side seven minutes from time.
The result leaves Swindon deep in relegation trouble and based on this performance they'll do well to escape the drop.