Bedene, who switched allegiance from Slovenia to Great Britain last month, won 86 per cent of his first service points to beat Argentina’s Maximo Gonzalez 6-3 3-6 6-3 in just under two hours.
The world number 99 will meet fellow qualifier Arthur de Greef in round two, the Belgian having recorded his first ATP win by saving two match points to beat eighth seed Diego Schwartzman, of Argentina, 4-6 7-5 6-4.
Pablo Andujar began his quest for a third Casablanca title, after victories in 2011 and 2012, by beating Tobias Kamke 6-3 6-4 and his next opponent will be sixth seed Andreas Haider-Maurer, a 6-2 6-7 (7/0) 7-6 (7/5) winner over Jan-Lennard Struff.
Former world number eight Mikhail Youzhny, playing at this tournament for the first time since 2002, brushed aside wild card Yassine Idmbarek 6-3 6-1 in 70 minutes and Damir Dzumhur hit nine aces to knock out 2007 champion Paul-Henri Mathieu 6-2 7-6 (7/2) to set up a last-16 meeting against fourth seed Marcel Granollers.
Wild card Nicolas Almagro, who is continuing his comeback from a foot injury, is now two match wins away from 250 clay-court victories after thrashing qualifier Taro Daniel 6-4 6-1 in 64 minutes.
Spain’s Daniel Gimeno-Traver beat Malek Jaziri, of Tunisia, 6-4 6-3 and Algeria’s Lamine Ouahab saw off Robin Haase, of Holland, 6-2 6-4.