Ukraine's Dolgopolov fell by the wayside at Devonshire Park in Eastbourne, England, after a 1-6, 6-3, 6-2 defeat at the hands of Spain's Fernando Verdasco.
Italy's Seppi -- runner-up at last year's event and its 2011 champion -- rallied from a first-set loss to get past French qualifier Guillaume Rufin 3-6, 6-3, 6-4.
Also moving on Monday was eighth-seeded Fabio Fognini of Italy, who clawed back for a 6-7 (6-8), 6-2, 6-4 victory over Slovenian Grega Zemlja.
Spaniard Albert Ramos, American qualifier Ryan Harrison and British wild card Kyle Edmund also notched wins on Day 1.
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