Andreev, seeded seventh and having just moved up three spots to 34th in the latest men's tennis rankings, took out Marcos Daniel 6-4, 7-5 on the opening day of the clay-court tournament.
No. 8-seeded Guillermo Canas was also a first-round winner Monday, defeating Ivo Minar 7-6 (11-9), 6-3.
In other matches Monday: Kristof Vliegen beat Martin Vassallo Arguello 6-3, 6-4; Guillermo Garcia-Lopez got by Michael Lammer 5-7, 6-3, 6-2; Florent Serra stopped Daniel Gimeno-Traver 7-6 (7-2), 7-6 (7-5); and Marin Cilic topped Josselin Ouanna 6-3, 6-4.
Stanislas Wawrinka, a local favorite, is the Swiss Open top seed while second-seeded Paul-Henri Mathieu is trying to defend his 2007 Swiss Open title.
The 2008 Swiss Open championship is worth $102,000.