Demetriou collected Wayne Gray's square pass to deliver a spectacular finish past Swindon goalkeeper Phil Smith for his sixth of the season.
Swindon, still in relegation trouble, were guilty of missing a host of chances as Orient goalkeeper Jamie Jones put in an outstanding performance to keep a clean sheet.
Orient stunned their hosts inside the opening five minutes when Gray capitalised on some lackadaisical play on the halfway line to burst down the left-hand channel.
The big striker looked up and played the ball into Demetriou's path. The Cyprus international took one touch to set himself and then curled his strike into the top corner.
Swindon attempted to force their way back into the encounter in a lively first 20 minutes as Orient defended resolutely from a series of Anthony McNamee crosses.
The Swindon winger picked out captain Gordon Greer on 12 minutes but his near-post header was just wide.
Four minutes later Owain Tudur-Jones delivered a fine free-kick that was bound for the top corner but Orient keeper Jones was equal to it, tipping the ball athletically over the bar.
Swindon continued their dominance in the final third in the second half as the impressive Hal Robson-Kanu breezed past Charlie Daniels and stood the ball up for Billy Paynter at the far post but, with the whole of the goal to aim at, the Town striker headed against the face of the crossbar.
Swindon's top scorer Simon Cox was enduring an off-day in front of goal as nothing seemed to go right for the in-demand striker.
However, he saw his first glimpse of goal, 13 minutes from time, when Paynter powered forward to roll the ball into his strike partner's path.
Cox beat Jones at his near post for the first time all afternoon but the ball rebounded back off the upright, hit the Orient goalkeeper and went out for a corner.