It's now three wins in the last four games for Cheltenham, while Orient have emerged from the Easter period without a point to show for their efforts.
The only goal arrived two minutes into the second half and Town could have won it by a wider margin, with Steven Gillespie hitting the bar twice in the second period.
It was a lively first 45 minutes and somewhat surprising that the teams went into the half-time break with nothing on the scoreboard.
Adam Boyd had the best chances for the visitors, sending two shots just wide and seeing another blocked on the line by Robins defender Jerry Gill.
At the other end, Scott Brown saw a firm shot deflected wide then fed Connor for a shot that hit the far post.
It was end-to-end stuff and Orient goalkeeper Glenn Morris had to dive full stretch to save from both Gillespie and Brown, although Cheltenham goalkeeper Shane Higgs followed suit shortly before the break, with a smart stop from Wayne Gray.
Connor's goal arrived just over 90 seconds following the re-start when a clearance by the Orient defence was headed back into the danger area by Cheltenham defender Andy Gallinagh.
Shane Duff got up well to flick it on and Connor took a touch before beating the advancing Morris with a cool finish.
Gillespie then hit the bar with two clever chip shots and Morris dived to save a shot from substitute Ashley Vincent, as Cheltenham looked to extend their lead.
The home side was almost left to regret not wrapping the game up when first Sean Thornton and then Gray went close with late efforts, but Cheltenham held on to complete their eighth win in 18 games since the turn of the year.