Murray and Zimonjic lost the first set 6-3 to German pair Daniel Brands and Florian Meyer but hit back to take the next 7-6 (7/5) on the tie-break.
That took the match into a champions tie-break and Murray and Zimonjic won that 10-8.
The world number four had returned to action in the Mubadala World Tennis Championship exhibition in Abu Dhabi on Boxing Day following back surgery.
The Wimbledon champion lost to Jo-Wilfried Tsonga before beating Stanislas Wawrinka to finish fifth in the exhibition tournament.
He had a minor operation on a long-standing back problem in September, bringing an early end to his season.
There was further British success in the Qatar Open doubles as Dominic Inglot and Treat Huey, of the Philippines, won their first round match 6-3 7-6 (7/4) against Alexandr Dolgopolov, of the Ukraine, and Russian Teymuraz Gabashvili.
Britain's Dan Evans enjoyed a rare victory in the men's singles qualifying round as he beat Japan's Taro Daniel in straight sets.
British number two Evans, who has failed to reach the same heights after making the third round of last season's US Open, won 6-2 6-2 to reach the main draw.
In the first round Evans will take on Latvian world number 24 Ernests Gulbis.