The Slovenia-born 28-year-old broke the lucky loser twice in the first set and then twice in the second to secure a convincing triumph within 69 minutes in Hamburg.
Next up for world number 46 Bedene is Russia's Karen Khachanov, who overcame Germany's Rudolf Molleker 6-4 6-3 in the first round.
Aljaz Bedene slips to defeat by Khachanov in Hamburg
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