Starting his second straight game and given a comfortable lead after the first, Jones stopped 28 shots for his first shutout since April 10, 2014. On Tuesday night, Jones was in the net when the Kings lost after a six-round shootout at Nashville.
Darcy Kuemper gave up all four first-period goals on 10 shots before being replaced by Niklas Backstrom to start the second.
Kuemper was 3-1-0 and had allowed just five goals in his previous four starts.
The blowout loss was Minnesota's second defeat at home and its most lopsided of the season.
Richards re-directed a shot that hit the post and bounced past Kuemper at 4:21 of the first. It was only the third time this season the defending Stanley Cup champions scored first on the road.
Brown and Toffoli followed with back-to-back, 2-on-1 goals.
Williams flicked a wrist shot past Kuemper to make it 4-0 with 10 seconds left in the period and send the Wild to the locker room as the hometown crowd booed.
The victory snapped a two-game losing streak for Los Angeles.
Entering Wednesday, the Wild had outscored opponents at home 32-16.
It was the second time Minnesota has been shut out this season and first at home since Jan. 14, 2014, against Ottawa.