The Blackhawks, who had the NHL's best record during the regular season, will try to fight off elimination when they host Game 5 on Saturday.
It was Howard's second career playoff shutout, the other one coming in 2010. He has started all of Detroit's post-season games over the last four seasons and improved his playoff record to 20-19.
Detroit moved to the brink of a spot in the Western Conference finals after barely making it into the playoffs during the final week of the campaign.
The Red Wings have won five of their last six post-season contests after falling behind 3-2 in the opening round against Anaheim.
Their only loss in the last six games came in the series opener against Chicago, in which the Blackhawks scored four times against Howard. Since then the Detroit goaltender has given up just two goals in 180 minutes of action.
Thursday's game was scoreless until Jakub Kindl scored his first goal of the playoffs midway through the second period. Kindl's tally came with Chicago's Jonathan Toews in the penalty box for high sticking.
That was the only goal Howard had to work with until Daniel Cleary scored into an empty net with 39 seconds to play.
Corey Crawford stopped 25-of-26 shots for the Blackhawks.