Tomic stopped Olivier Rochus 6-4, 6-3 by winning two-thirds of the points on serve in his first-round match. He pounded out nine aces. He did lose his serve once but didn't see a break point in the second set.
Giraldo won by the identical score, beating Steve Darcis.
World No. 5 Jo-Wilfried Tsonga is the No. 1 seed for the tournament. The top four seeds were given first-round byes.
Nikolay Davydenko, seeded seventh this year, won the BMW Open last year with a three-set victory over Florian Mayer.
The 2012 BMW Open winner will take home about $95,000.
Notable deaths of 2014 [PHOTOS]