The big-serving South African, who towers over his 30-year-old Belgian opponent, sent down 12 aces and broke Rochus' serve four times.
Anderson, ranked 35 in the world, now faces a daunting prospect in the second round: second seed Novak Djokovic, undefeated in 27 matches this year.
German Florian Mayer, losing finalist on Sunday in Munich to Nikolay Davydenko, upset Serb 16th seed Viktor Troicki 4-6, 7-5, 6-4, but Davydenko went down to Spain's Marcel Granollers 7-5. 6-2.
In other first-round action on Tuesday, Gilles Simon beat Ivan Ljubicic 7-5, 7-6.
Jo-WilfiredTsonga, who took out 10th seed Nicolas Almagro in the first round, was the first player through to the third round, beating qualifier Pere Riba 6-4, 6-2.
Results from the Madrid Open at the Caja Magica tennis center (seedings in parentheses):
Men
Singles
First round
Marcel Granollers, Spain, def. Nikolay Davydenko, Russia, 7-5, 6-2.
Florian Mayer, Germany, def. Viktor Troicki (16), Serbia, 4-6, 7-5, 6-4.
Thomaz Bellucci, Brazil, def. Pablo Andujar, Spain, 6-4, 6-2.
Gilles Simon, France, def. Ivan Ljubicic, Croatia, 7-5, 7-6 (8).
Kevin Anderson, South Africa, def. Olivier Rochus, Belgium, 6-2, 6-4.
Juan Martin del Potro, Argentina, def. Mikhail Youzhny (13), Russia, 6-1, 3-6, 6-3. ^Second Round=
Jo-Wilfried Tsonga, France, def. Pere Riba, Spain, 6-4, 6-2.
Women
Singles
Second round
Samantha Stosur (5), Australia, def. Daniela Hantuchova, Slovakia, 7-6 (1), 7-5.
Bethanie Mattek-Sands, United States, def. Vania King, United States, 6-0, 6-2.
Petra Kvitova (16), Czech Republic, def. Chanelle Scheepers, South Africa, 6-3, 6-3.
Caroline Wozniacki (1), Denmark, def. Bojana Jovanovski, Serbia, 6-4, 6-4.