Formula E title to be decided in potentially dramatic finale on Sunday in Seoul
New Zealander Evans won Saturday's first race of the double-header for Jaguar, after seizing the lead into the first corner from third on the grid, with Belgian Vandoorne fifth at Seoul's Olympic Stadium.
The first E-Prix held in the South Korean capital ended behind the safety car after a late crash involving Mahindra's Alexander Sims.
Former McLaren Formula One driver Vandoorne now has 195 points to Evans' 174 with Mercedes also leading the teams' standings.
Vandoorne will be champion if he finishes at least seventh on Sunday.
DS Techeetah's double champion Jean-Eric Vergne and Venturi's Edoardo Mortara dropped out of mathematical title contention in a race that started on a damp and slippery track and was red-flagged after an early eight-car pileup.
Outgoing champion Nyck de Vries was one of those involved, escaping unhurt after his Mercedes was trapped under the Nissan of Swiss driver Sebastien Buemi.
"This morning was tricky. We didn't quite have the pace but the rain came at the right time and I qualified up front," said Evans after his fourth win of the season.
"The race was really hard to manage, the conditions changed all the time ... this is what we needed, we'll go to tomorrow and keep fighting," added the Jaguar driver, who has managed back-to-back victories before.
British driver Oliver Rowland finished second on Saturday for Mahindra, after starting on pole, with Brazilian Lucas di Grassi third for Venturi.