Swindon got off to a dream start with Thomas Dossevi giving them the lead after only 50 seconds with a close range header.
Swindon then went close to getting a second before Dagenham started to come back into it in the first half.
Dagenham then equalised on 48 minutes with a goal from Damian Scannell.
Swindon then went on to have a number of corners, but didn't come close to scoring before in the 80th minute Dagenham took the lead with a goal from Savage after Swindon had failed to clear the ball away.
This defeat now leaves Swindon in 16th place. Swindon now have a break from the league as they face Torquay at home at 7pm on Tuesday night in the Johnstone's Paint Trophy.