Andreev has gone three rounds at the Australian Open, but the Russian said on Tuesday he "wasn't playing my best tennis.''
He also complimented Dodig, a Croatian who secured his first win on the main ATP Tour in 75 minutes.
Third-seeded Juergen Melzer of Austria and eighth-seeded Simone Bolelli of Italy also lost, while defending champion Sergiy Stakhovsky of Ukraine won his opener.
Evgeny Korolev of Russia beat Melzer, 6-4, 6-0, Viktor Troicki of Serbia downed Bolelli 6-3, 6-4, and Strakhovsky, who won the 2008 title as a lucky loser, beat veteran Dominik Hrbaty of Slovakia 6-2, 4-6, 6-1.
Third-seeded Ivo Karlovic served 15 aces in beating Philipp Petzschner of Germany 6-3, 6-3, and another Croatian seed, No. 7 Mario Ancic, needed 2 hours, 22 minutes to overcome Lukas Lacko of Slovakia 6-4, 6-7 (6), 7-5.
Ancic blew a 4-2 lead in the second set, and had to save three break points at 4-4 in the third.
"That was a very hard duel,'' he said.
Also, Jan Hernych of Czech Republic and Ernests Gulbis of Latvia were winners.
Top seed Andreev stunned by outsider at Zagreb
Player Ratings: Numancia 0-2 Real Madrid
