Vinciguerra overcame a 6-7 (5-7) loss in the first set against Florent Serra but came back to oust the sixth-seeded Frenchman by taking the next two sets 6-3, 6-4 on Bastad's red clay courts.
Likewise, Gabashvili fell behind with a 4-6 loss in the first set to seventh-seeded Belgian Christophe Rochus, then rallied to victory by winning the next two sets 6-1, 6-0 .
In another first-round match, Romanian Victor Crivoi eliminated Uzbekistan's Denis Istomin 6-0, 6-4.
Spaniard Fernando Verdasco, Swede Robin Soderling and reigning champion Tommy Robredo of Spain are this event's top seeds. Robredo defeated Czech Tomas Berdych for last year's title and also won here in 2006.