The 28-year-old rallied from a set down to win the next two when rain interrupted the match. The Indian, however, returned to complete the job as he emerged 4-6, 6-1, 6-2, 4-6, 6-4 victories in the match which lasted three hours and 11 minutes at Flushing Meadows last night.
The world number 114 Indian will next take on Italian Andrea Seppi, ranked 20th, in the second round. Seppi beat Belgian veteran Xavier Malisse 6-3, 3-6, 7-5, 7-5 in another men's singles match.
Somdev won 93 per cent of the net points compared to Lukas's 63 per cent and also converted eight of the 12 break points that came his way.
He also committed just 36 unforced errors, while Slovak had double the number of unforced errors (73) in the match.
The Indian, who was laid low for more than a year after suffering a shoulder injury, won more than 50 per cent of points when serving at 30-30 or Deuce.
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