The second seed, who won at Queens and reached the fourth round at Wimbledon, easily made the transition back onto clay and wrapped up the win in under an hour.
Cilic lost in last year's final to third seed Alexandr Dolgopolov with Spain's Fernando Verdasco the top seed this time out.
In Stuttgart, top seed Janko Tipsarevic had a similarly comfortable start as he beat Belgium's Steve Darcis 6-4 6-2.
Like Cilic in Croatia, Tipsarevic received a bye into the second round and will now face Bjorn Phau in the last eight of the 28-man clay court tournament.
At the grass court event in Newport, top seed and defending champion John Isner beat Nicolas Mahut 6-2 7-6(2) in the second round - a rematch of their Wimbledon epic from 2010.
Second seed Kei Nishikori was less convincing but avoided a scare as he beat Belgium's Olivier Rochus 6-7(6) 6-4 6-2 in the second round, while veteran Australian Lleyton Hewitt saw off home hope Tim Smyczek 6-4 2-6 6-1.
At the clay event in Bastad, Sweden top seed David Ferrer safely made it into the quarter-finals with a 6-4 6-3 win over Simone Bolelli but fourth seed Jarkko Nieminen and seventh seed Filippo Volandri both lost to Jan Hajek and Juergen Zopp respectively.