The pair shed the rest of their companions from a big early breakaway group before battling one-on-one for the stage victory in Ortisei, where van Garderen proved stronger in the closing metres.
Behind the breakaway, it was an aggressive day for the GC contenders, with Movistar's Nairo Quintana and Bahrain-Merida's Vincenzo Nibali both trying to drop race leader Tom Dumoulin (Sunweb). Quintana made a powerful dig on the Passo Gardena that Nibali ultimately joined, but Dumoulin refused to allow his rivals much breathing room, closing down the move before the top of the climb.
After further moves by Quintana and Nibali were reeled in, FDJ's Thibaut Pinot got away on the final climb and took back over a minute on the rest of the GC riders. Dumoulin, Nibali and Quintana all arrived at the finish line together.