Dodig, the defending champion and No. 4 seed this year, topped Guillermo Garcia-Lopez 4-6, 6-4, 6-4 in a 2 1/2-hour battle. Dodig lost his serve twice in the first set but had a pair of third-set breaks to improve to 2-0 lifetime versus Garcia-Lopez.
Their other meeting was in the Zagreb Indoors semifinals last year and also went three sets.
Karlovic lost just 11 points in eight service games of a 6-3, 6-2 win over Dudi Sela. Karlovic saved the only break point he faced and had a pair of breaks in each set.
Lukas Lacko ousted No. 2-seeded Alex Bogomolov Jr. in a seesaw 6-0, 6-7 (1-7), 6-1 decision. Lacko won two-thirds of the points over the first and third sets.
Other second-round matches Thursday saw third-seeded Mikhail Youzhny top Grega Zemlja 6-1, 6-3 and No. 6-seeded Marcos Baghdatis defeat Lukasz Kubot 6-4, 6-2.
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