With the shutout on a windy and chilly day, the expansion Sounders became the first team in MLS history not to allow any goals in their first three games.
Ljungberg began the scoring with a goal in the 15th minute and Zukani scored in the 44th.
Lundberg scored on a swirling shot into the penalty area, which fell to the feet of Sounders striker Nate Jaqua.
Later, Zukani, a former first-team all-American at Akron and the first overall pick in last January's SuperDraft, booted a shot past Reds netminder Greg Sutton, the game's last goal.
Goalie Kasey Keller made three saves in his third straight scoreless encounter.
The Sounders have outscored their first three opponents by a 7-0 margin.
The Reds (1-1-1) had picked up four points in two road matches.
Copyright 2009 by United Press International.
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