Cilic got by Paolo Lorenzi 6-1, 6-7 (6-8), 4-6, 6-3, 6-2 in 3 hours, 43 minutes. Seppi came back with a 6-2, 6-7 (2-7), 6-4, 6-4 win over Ivan Dodig a 3-hour match.
The first-round series turns to doubles Saturday, with Lorenzi and Simone Bolelli scheduled to go against Croats Nikola Mektic and Mate Pavic.
Friday's winners -- Seppi and Cilic -- have the first singles match Sunday, with Dodig to take on Fabio Fognini in the final series of the match.
The winning team qualifies for the Davis Cup quarterfinals, where it will play the winner of a series sending Spain against Canada.
Lorenzi filled in for Fognini, who was hit by a case of the flu, Friday and played the higher-ranked Cilic even for four sets. While Cilic jumped ahead with two fifth-set breaks, Lorenzi was able to come back to make Cilic work for the win.
The statistics don't suggest the match was that tight, as Cilic dropped serve just once -- costing him the third set. He had 72 unforced errors and was able to cash in five of his 15 break-point chances.
Seppi had six breaks in his win, with at least one in each set, but lost his own serve only twice -- once in the second set, leading to the loss in the tiebreaker, and once in the fourth set when Seppi countered with two breaks and won the match.
Swim Week Miami Beach 2014 [PHOTOS]