QPR had dominated the game in which Norwich were awarded a first-half penalty before the referee reversed his decision, but Russell struck with just over 20 minutes to go.
The hosts should have taken the lead inside the first minute when Dexter Blackstock combined with strike partner Heidar Helguson, but the Icelandic striker pulled his shot wide of the far post.
Spanish debutant Jordi Lopez went close with a long-range free kick, before Blackstock saw his deflected effort go wide of David Marshall's post.
Against the run of play the visitors thought they should have had a spot kick on 32 minutes when Lopez appeared to bring down Lee Croft in the box.
Referee Graham Scott - who was taking charge of his first game in the Championship - pointed to the spot and then changed his mind after consulting with his assistant.
But Norwich made up for it when Russell capitalised on some poor defending to send Wes Hoolahan's ball into the back net.
Russell's shot trickled past Radek Cerny in the Rangers goal but the driving rain made it difficult for the keeper and the win gave Bryan Gunn's side a much needed three points.