Froome, 31, was over six minutes behind the Dutch winner on a tortuous stage in the Pyrenees but finished alongside his main rivals, including fellow Briton Adam Yates, who stays in second place.
In heavy rain, Dumoulin (Team Giant-Alpecin) finished 38 seconds ahead of Rui Costa and Rafal Majka in Andorra.
Earlier, two-time Tour winner Alberto Contador quit the race through illness.
Yates, 23, remains in the young riders' white jersey, while Mark Cavendish is still in the sprinters' green jersey despite a day spent at the back of the peloton.
After the 184.5km stage, which started in Spain and comprised three category one climbs and the first mountain-top finish this year, the riders will take a rest day on Monday before resuming on Tuesday.
In the race for the king of the mountains, France's Thibaut Pinot (FDJ) took the polka dot jersey from Poland's Majka (Tinkoff).
