Baghdatis, who reached the quarter-finals in Indian Wells seven years ago, was dumped out 6-0 7-6(3) by his German opponent.
Next up for Brands is Andreas Seppi of Italy.
Former world number one Lleyton Hewitt, twice a winner in Indian Wells, booked a date with 2012 runner-up John Isner after beating Lukas Rosol.
The Australian took an hour and 35 minutes to secure the 6-4 3-6 6-1 win, during which he converted four of 12 break points.
Hewitt won the title in 2002, when he defeated Tim Henman in the final, and a year later with victory over Gustavo Kuerten.
Fellow Australian Bernard Tomic, ranked 45 in the world and holder of one title already this season - Sydney - kicked off the day's play at Indian Wells Tennis Garden with a 6-4 6-3 win over Thomaz Bellucci of Brazil to set up an intriguing second-round encounter with Richard Gasquet.
David Nalbandian stuttered slightly in his first-round encounter with Marcel Granollers but the Argentine former world number three managed to save seven of eight break points to progress 6-4 6-2.
World number 37 Kevin Anderson also registered a straight-set win, 7-6(6) 6-3 over Victor Hanescu as the South African continues his comeback from elbow surgery. Anderson is now 10-3 so far this season.
Serbia's Viktor Troicki was upset by David Goffin, the Belgian claiming his third tour victory of the year with a 4-6 6-3 6-4 win. It is Goffin's first appearance at the Californian event.
The seeded players at the tournament have byes into the second round. The world's top players, including Rafael Nadal, will all be in action later in the week.
BNP Paribas results
Ryan Harrison (U.S.) beat Go Soeda (Japan) 6-0 4-6 6-3
Ernests Gulbis (Latvia) beat Feliciano Lopez (Spain) 6-3 6-2
Ivan Dodig (Croatia) beat Guido Pella (Argentina) 6-1 6-2
Lleyton Hewitt (Australia) beat Lukas Rosol (Czech Republic) 6-4 3-6 6-1
Denis Istomin (Uzbekistan) beat Vasek Pospisil (Canada) 7-6(5) 6-3
Wayne Odesnik (U.S.) beat Roberto Bautista (Spain) 7-5 7-5
Mischa Zverev (Germany) beat Jurgen Melzer (Austria) 3-6 6-3 7-6(3)
Daniel Brands (Germany) beat Marcos Baghdatis (Cyprus) 6-0 7-6(3)
David Nalbandian (Argentina) beat Marcel Granollers (Spain) 6-4 6-2
Kevin Anderson (South Africa) beat Victor Hanescu (Romania) 7-6(6) 6-3
Leonardo Mayer (Argentina) beat Xavier Malisse (Belgium) 6-2 3-6 6-4
Jarkko Nieminen (Finland) beat Igor Sijsling (Netherlands) 4-6 6-3 6-3
Benoit Paire (France) beat Lukasz Kubot (Poland) 5-7 7-5 6-2
David Goffin (Belgium) beat Viktor Troicki (Serbia) 4-6 6-3 6-4
Paolo Lorenzi (Italy) beat Gilles Muller (Luxembourg) 7-5 6-4
Bernard Tomic (Australia) beat Thomaz Bellucci (Brazil) 6-4 6-3