Ivan Klasnic and Eduardo scored as Croatia stayed in second place in World Cup qualifying Group Six.
However, Croatia will rue the fact they could not score more goals against the group's bottom side who have yet to claim a point.
The match was interrupted twice by the visiting fans who threw flares on to the pitch in Andorra La Vella.
Croatia threatened from the start and had a great early chance when Darijo Srna received the ball from Ivan Rakitic on the left side and attempted a volley which went narrowly over.
However, they opened the scoring in the 15th minute following some neat combination play between Rakitic and Klasnic who sent a shot across goalkeeper Jesus Alvarez and into the net.
The visitors then forced a series of corners but they came to nothing before Brazilian-born Eduardo doubled the lead in the 35th minute.
Hrvoje Cale began the move passing to Klasnic who turned the ball into the path of the Arsenal striker who ran quickly on to the ball and converted for 2-0.
However, the game was interrupted in the 39th minute when flares were thrown on to the pitch by some Croatia fans outside the ground causing the game to be stopped for three minutes.
Croatia manager Slaven Bilic tried to appease those fans but just a minute after the start of the second half, another set of flares were thrown prompting a brief interruption.
In the second half Croatia dominated possession but they could not force an opening and were forced to settle for just the two-goal victory.
The result leaves the Croatians five points behind England but three ahead of Ukraine with the teams set to meet in Zagreb in their next games in June.