Japan suffered major blows before the 24-team event with the withdrawals of injured star Kei Nishikori and world number 81 Yasutaka Uchiyama, their third best player.
But the strong performances of Nishioka and Go Soeda will have served notice for opponents in Group B, much to the delight of the sparse Perth crowd mainly comprised of Japanese fans.
Japan have already clinched the tie ahead of the doubles.
World number 73 Nishioka put on a masterclass over a dispirited Cuevas, but was helped by his lacklustre opponent who did not hit a winner during a grim first set.
The left-handed Nishioka caused the world number 45 problems with an array of menacing slices mixed with swift movement around the court.
New tennis era kicks off with ATP Cup
Cuevas finally hit the scoreboard in the sixth game of the second set but Nishioka soon closed out the one-sided contest in just 54 minutes.
"I don't have much power compared to other players, so I have to use my footwork," 24-year-old Nishioka said.
"I think last year I improved, so this year I will try to be a little more aggressive and use my strengths."
Martin Cuevas, Pablo's younger brother, fared only slightly better in the earlier match after Soeda, ranked 121, put Japan ahead with a comfortable 6-1, 6-3 victory in 76 minutes.
The 35-year-old was too consistent for world number 523 Cuevas, who was broken three times in the first set.
Soeda had replaced world number 13 Nishikori, who withdrew from the tournament and the Australian Open with an elbow injury.
Cuevas put up more of a fight in the second set but appeared hampered by a hamstring issue and received medical treatment after the seventh game.
"I was really nervous in the beginning but I had a plan and it worked well," Soeda said.
Rafael Nadal-led Spain play Georgia in the later Group B tie.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ