Signed as a free agent to replace the retired Dominik Hasek, Joseph denied All-Star Alex Zhamnov on a shorthanded breakaway midway through the first period and turned aside all 24 shots over the first period.
Steve Sullivan ended Joseph's shutout bid with 16:01 left in regulation when he banked a backhander from along the goal line off the goaltender's skate and into the net.
Detroit had a chance to win, but highly touted rookie Henrik Zetterberg shot wide of an open net with 7:54 to play in the third period.
Two-time Norris Trophy winner Nicklas Lidstrom scored the Red Wings' lone goal on a shorthanded one-timer late in the second period.
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