The Devils held a 2-1 lead until 1:02 was left in the second period, when Eric Brewer scored to pull the Blues even.
Winchester then notched the only goal in the final frame and St. Louis remained undefeated at home in regulation time at 8-0-1.
Alex Pietrangelo collected the Blues' other goal and Jaroslav Halak stopped 35 shots for the victors.
New Jersey, which dropped its fifth game in six contests, got goals from David Clarkson and Mattias Tedenby.
The Devils also got more bad news Saturday when it was reported veteran goalie Martin Brodeur may be out two weeks with a right elbow injury.
St. Louis native Mike McKenna subbed for Brodeur and took the loss, letting in three goals on 27 shots.