Rusedski needed just 68 minutes, producing 14 aces in the first set and losing a single point in his last four service games. He will now play either the defending champion, Thomas Enqvist, or Magnus Larsson.
The world No 5 showed he intended to go flat-out against Florida-based Roux, 71st in the world, as he went full-steam through the warm-up. Rusedski earned a break in the ninth game of the opening set and served out for 6-4 after 29 minutes.
The second set stayed with serve but Rusedski rallied from 1-4 down in the tie-break, fired over a service winner to yield a match point and hit a winning volley for the victory.
Henman faces a quarter- final today against the top seed and US Open champion, Patrick Rafter, of Australia.
Rusedski's service was his biggest weapon, accounting for 20 aces. He lost only seven points on service - two in the second set - and his first eight points of the match came from a barrage of aces.
"I was pleased with my serve - it made the difference today," he said. "I cannot complain. I felt terrible for the past two days, but I just stayed in bed and slept.
Rusedski refused to look ahead to a meeting with Henman. "I don't even want to think about a possible final with Henman - there are too many good players to get past. I'm excited about Hanover, but I'm not worried about expending too much energy here. I'll be going back to bed today to rest some more. I've got a tough draw ahead of me and I want to be ready."Reuse content