Alberto Contador of Spain outsprinted Rasmussen to the wire, completing the 119-mile leg from Mazamet to Plateau-de-Beille in the Pyrenees in five hours, 25 minutes and 48 seconds.
Rasmussen remained the overall leader, however, by two minutes, 23 seconds over Contador. Australia's Cadel Evans is third, 3:04 behind, but he lost time on Sunday and swapped places with Contador after a seventh-place finish.
American Levi Leipheimer finished fourth, 40 seconds behind the top two, and moved into fourth overall. He is 4:29 behind Rasmussen.
Germany's Andreas Kloden is fifth overall, 4:38 off the lead pace.
Sunday's stage, the first of three in the Pyrenees with a rest day thrown in, featured three climbs.