Cummings’ compatriot Mark Cavendish had already won three of the first six stages for the African outfit.
South African Daryl Impey took second on the stage ahead of David Navarro of Spain.
Belgian Greg Van Avermaet finished fifth and extended his overall lead in the yellow jersey competition ahead of Frenchman Julian Alaphilippe and Alejandro Valverde of Spain.
But there was controversy when the peloton of leading contenders arrived to find the inflatable arch indicating the final kilometre had collapsed, taking down another Briton, Adam Yates, as he passed beneath it.
The 23-year-old Orica rider eventually finished the stage with blood on his chin.
The expected fireworks on the first major climb of this year’s Tour never materialised, though, as the favourites, including reigning champion Chris Froome and Colombian Nairo Quintana, made no attempts to attack each other.
But French hope Thibaut Pinot suffered badly on the climb and lost around 2min 30sec.
For Cummings, an Olympic silver-medallist and world champion from the track in the team pursuit, it was a second stage victory in successive years.
