Lippert profited from many of her rivals falling on the wet roads of the Cantal region including Dutchwoman Eva van Agt who suffered a concussion after crashing against a security barrier while leading, four kilometres from the line.
Movistar's Lippert pipped Kopecky on the line, timing four hours, 13 minutes and 43 seconds after the 151km run from Clermont-Ferrand to Mauriac in the Auvergne region of south-central France.
"It was a very intense day from the start and ultimately chaotic, but I was well placed by my team," said Lippert, who was "relieved to have avoided falls".
As a track specialist, Kopecky demonstrated her skills in slippery conditions, particularly in the last hour of racing and even survived a puncture in the final straight.
"I lacked grip in the last metres. I understood why when I discovered after the line that my rear wheel was flat," she explained.
Dutch riders Yara Kastelijn, Anouska Koster and Van Agt, made a break with 40km to go but were caught in the final bends of a chaotic finale.
Defending champion Annemiek van Vleuten, the Dutch race favourite, took a tumble on the Plaines climb, the main difficulty of the day 46km before the line.
Kopecky leads Lippert by 49sec in the overall standings with van Vleuten slipping to nearly a minute behind the leader.
Tuesday's 147.2km third stage should suit the sprinters between Collonges-la-Rouge and Montignac-Lascaut in Dordogne.