Andujar, who bested Albert Ramos during last year's all-Spanish finale in Casablanca, didn't get nearly that far this time, getting bounced by fellow Spaniard Pablo Carreno-Busta 6-4, 2-6, 6-3.
Meanwhile, Austria's Melzer was upended by German Tobias Kamke in straight sets 6-3, 6-3 on the clay courts of Complexe Al Amal.
Avoiding the upset bug, meanwhile, was eighth-seeded Grega Zemlja of Slovenia, who had to battle to get past Germany's Matthias Bachinger 6-7 (3-7), 7-5, 7-6 (7-2).
Other first-round winners Tuesday included Swiss qualifier Henri Laaksonen, Slovenian Aljaz Bedene, Italian qualifier Filippo Volandri and France's Edouard Roger-Vasselin.
2014: The Year in Music [PHOTOS]