There was a scarcity of goalmouth action in a forgettable opening 45 minutes, with the only effort on goal at either end a tame header from Dungannon's Cahal McGinty which was straight at Glentoran goalkeeper Andrew Mills.
As the rain worsened in the second half, Glentoran went close when the ball broke kindly for Danny Amos and his snapshot fizzed narrowly over the crossbar.
At the other end, McGinty again connected with a Knowles free-kick, but his header dropped onto the top of the Glentoran net.
Glentoran almost went in front in fortuitous circumstances as Tiarnan Kelly almost diverted Danny Amos' corner into his own net, but Declan Dunne scooped the ball clear off the goal-line.
The home side also had penalty appeals waved away after a robust challenge by Danny Wallace on Singleton inside the area.
The deadlock was eventually broken on 68 minutes when Knowles' corner was inadvertently headed into his own net by Singleton, with keeper Mills unable to scramble the ball clear at the post.
The Swifts almost doubled their advantage when Sean McAllister's curling effort was tipped over the crossbar by Mills.
It went from bad to worse for Glentoran on 78 minutes as substitute Rusell was shown a straight red card by referee Shane Andrews after deliberately bringing down Steven Scott to halt a Dungannon counter-attack.