The Croat fired 18 aces in a 7-6 (3) 7-6 3) win against the Bulgarian in a match where neither player could even manufacture a break point.
Karlovic is a three-time quarter-finalist at his hometown event.
Fifth seed Martin Klizan came from a set down against Matteo Viola to reach the second round
The world number 33 was broken twice in a first set that he lost 6-4 before edging a second-set tiebreak to narrowly avoid an upset against 148th-ranked Italian Viola.
The relieved Slovak dominated the deciding set to win 4-6 7-6(6) 6-1.
Left-hander Klizan, 23, raced up the rankings in 2012 after a run to the second round of the French Open saw him break into the top 100.
Reaching the fourth round of the US Open - upsetting fifth-seeded Frenchman Jo-Wilfried Tsonga in the second round - he then won his first ATP tournament in St Petersburg, beating Fabio Fognini in the final.
Viola, 25, reached a career-high ranking of 123 in November last year.
The top four seeds in Croatia - Marin Cilic, Andreas Seppi, Mikhail Youzhny and Juergen Melzer - all received byes into the second round.
Top seed Cilic knocked Klizan out 7-5 6-4 6-0 in that US Open fourth-round match.
In Montpellier, crowd favourite Gael Monfils and eight seed Benoit Paire rewarded the home fans with straight set wins but ninth seed Paul-Henri Mathieu was beaten by Sergiy Stakhovsky.
ATP Zagreb first-round results
Lukas Rosol (Czech Republic) beat Filip Veger (Croatia) 6-2 6-4
Ivo Karlovic (Croatia) beat 7-Grigor Dimitrov (Bulgaria) 7-6(3) 7-6(3)
Grega Zemlja (Slovenia) beat Ilija Bozoljac (Serbia) 6-7(5) 7-6(4) 6-2
Blaz Kavcic (Slovenia) beat Aljaz Bedene (Slovenia) 6-7(5) 6-3 6-3
Philipp Petzschner (Germany) beat Mate Pavic (Croatia) 7-5 6-2
Igor Sijsling (Netherlands) beat Nikola Mektic (Croatia) 6-4 6-2
Somdev Devvarman (India) beat Michael Berrer (Germany) 0-6 7-6(6) 4-1 (Berrer retired)
5-Martin Klizan (Slovakia) beat Matteo Viola (Italy) 4-6 7-6(6) 6-1
ATP Montpellier first-round results
Sergiy Stakhovsky (Ukraine) beat 9-Paul-Henri Mathieu (France) 6-4 6-4
Gael Monfils (France) beat Ruben Bemelmans (Belgium) 7-5 6-4
8-Benoit Paire (France) beat Adrian Menendez (Spain) 6-0 6-2
Victor Hanescu (Romania) beat Guillermo Olaso (Spain) 6-1 7-6(6)
Jarkko Nieminen (Finland) beat Florent Serra (France) 6-3 6-2
Jan Hajek (Czech Republic) beat Dudi Sela (Israel) 2-6 7-5 6-1
Steve Darcis (Belgium) beat Adrian Mannarino (France) 6-4 7-6(0)
ATP Vina del Mar first-round results
Albert Montanes (Spain) beat Nicolas Massu (Chile) 6-7(6) 6-3 6-4
Horacio Zeballos (Argentina) beat Diego Schwartzman (Argentina) 1-6 6-2 6-2
Federico Delbonis (Argentina) beat Guido Pella (Argentina) 2-6 7-6(4) 7-6(1)
Tommy Robredo (Spain) beat Pere Riba (Spain) 6-2 6-2
8-Carlos Berlocq (Argentina) beat Andrey Kuznetsov (Russia) 6-2 6-1
Guillaume Rufin (France) beat Ruben Ramirez Hidalgo (Spain) 6-3 6-4
Christian Garin (Chile) beat Dusan Lajovic (Serbia) 6-3 6-4
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