Vinokourov, who won last Friday's time trial, broke away near the end of Monday's 122.5-mile route from Foix to Loudenvielle-Le Louron to take the stage in 5 hours, 34 minutes and 28 seconds. That time was 51 seconds better than Kim Kirchen and Haimar Zubeldia.
Monday's stage included five major climbs and was considered one of the toughest of the more than 2,200-mile Tour de France this year.
Rasmussen finished 11th in Monday's stage about 5 1/2 minutes behind the leader but kept his 2:23 lead over Alberto Contador in the overall standings. He had a 4-minute advantage over third-place Cadel Evans and a 5:25 lead on Levi Leipheimer, who is in fourth.
Tour racers have the day off Tuesday before five consecutive days of stages complete the race. The final stage is Sunday in Paris.