As she won the Australian Open earlier this year and took over the No. 1 ranking, Azarenka looked liked she might be the woman to break a long string of disappointing top players.
Ross converted both scores but they trailed at the break as Jones punished a string of infringements with three penalties to give the visitors the half-time advantage.
But Safin did not have to stretch himself much to seal the set, Lopez making a string of unforced errors to lose the tie-break 7-1 and fall 2-1 behind in sets.
Sudan, who have come with a second-string team, were kept under pressure but managed to break on a counter-attack to restore their lead 10 minutes later through Amarria.