Tipsarevic and Monaco are the Stuttgart event's top seeds.
The Serbian battled for nearly 3 hours to eliminate Germany's Bjorn Phau 6-7 (6-8), 7-6 (7-2), 6-4.
Monaco, of Argentina, bidding for his third clay-court title of the year, defeated Slovenian Pavol Cervenak 6-1, 7-5.
Tipsarevic will play Brazil's Thomaz Bellucci and Monaco takes on Spaniard Guillermo Garcia-Lopez in the semis Saturday.
Bellucci advanced with a 6-4, 6-1 victory over German Cedrik-Marcel Stebe and Garcia-Lopez ousted another German, Dustin Brown, 6-0, 6-3 in the quarterfinals.
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