Chicago built a 2-0 advantage in the Western Conference quarterfinal series, which now moves to Minnesota for the next two games on Sunday and Tuesday.
Frolik produced the only first-period goal and then scored shorthanded just 49 seconds into the middle period.
Minnesota got one goal back on a wrist shot by Devin Setoguchi late in the second, but Sharp then delivered two goals in the third period to put the Blackhawks in command.
Chicago had to go to overtime before downing the Wild in the series opener, but the Blackhawks dominated Game 2 by outshooting Minnesota 47-28.
Corey Crawford made 28 saves and his second victory in these playoffs equals the total he had a year ago when Chicago was knocked out in the first round. This is Crawford's fourth trip to the postseason and he has yet to lead the Blackhawks into the second round.
Josh Harding, the Wild's backup goalie who has started both playoff games because of a lower-body injury experienced by Niklas Backstrom during warmups before Game 1, faced a game-long assault and gave up four goals on 47 shots.