Howard was especially tough down the stretch, turning aside 16-of-17 shots in the final period as the Blackhawks struggled to notch the equalizer after going down 2-0.
Moments later, Chicago's Andrew Shaw appeared to have tied the contest but his goal was waved off due to goalie interference.
Pavel Datsyuk then netted an insurance tally for the seventh-seeded Red Wings, who took control of the best-of-seven series.
Corey Crawford made 27 saves for the top-seeded Blackhawks, who will attempt get back into the series in Thursday's Game 4.
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