Portugal lacked many stars, including the biggest one of all Cristiano Ronaldo, having won 2-1 at home against Serbia just 48 hours earlier in a Euro 2016 qualifier.
The Blue Sharks scored twice within six minutes close to half-time at Estadio Antonio Coimbra da Mota for a rare away victory over European opposition.
An Odair Fortes cross found the corner of the net on 38 minutes and Gege tapped the ball over the goal-line at the far post to double the lead to seal a win over a side that had four players making their debuts.
Former Portuguese colony Cape Verde comprises a string of islands off the coast of Senegal and has just 500,000 inhabitants.
The Sharks are ranked 38 in the world — 31 places below Portugal — and made a first-round exit from the 2015 Africa Cup of Nations in Equatorial Guinea after three consecutive draws.
Ghana and Mali drew 1-1 at Stade Sebastien Charlety in southern Paris, enabling both countries to avoid suffering two straight losses during the international window.
Emmanuel Agyemang-Badu, who has not scored for Serie A outfit Udinese this season, put the 2015 Cup of Nations runners-up ahead on 53 minutes.
He nudged a through ball past Soumaila Diakite and then ran past the fallen goalkeeper to tap the ball into the net.
Bakary Sako from English second-tier promotion contenders Wolves levelled by converting a 71st-minute penalty needlessly conceded when Richmond Boakye fouled Molla Wague.
Malian Modibo Maiga rattled the crossbar during the first half and Boakye struck the post after half-time.
Mali lost 4-3 to Gabon last Wednesday and Ghana fell 2-1 to Senegal three days later.
A stoppage-time equaliser from Yu Dabao forced Tunisia to settle for a 1-1 draw with China in the Nanjing Olympic Sports Centre stadium.
After conceding a couple of late goals to lose 2-0 in Japan, the Tunisians looked set for victory having taken the lead on 39 minutes.
Substitute Mohamed Ali Moncer crept unnoticed to the far post and gave the Chinese goalkeeper no chance with a powerful header.
Saber Khalifa wasted a chance to double the advantage soon after half-time as his penalty was blocked and he fired the rebound wide.
Democratic Republic of Congo, who exceeded expectations with a third-place Cup of Nations finish, were the only African team to lose both friendlies.
A 1-0 defeat by Iraq at Khalid Bin Mohammed Stadium in Sharjah followed a 2-1 loss to the same country three days ago at another United Arab Emirates venue.
Yaser Kasim from English third-level side Swindon Town scored the winner on the hour, running across the field just outside the box before unleashing an unstoppable rising shot.
Corentin Martins celebrated his first success since succeeding fellow Frenchman Patrice Neveu as coach of Mauritania with a 2-0 victory over Niger in Nouakchott.
After 73 goalless minutes at Stade Olympique, Adama Ba put the hosts ahead from a penalty and Ali Abeide added a second soon after.
Moussa Konate, whose two goals sank Ghana last Saturday, was on target again as Senegal won 2-1 at French Ligue 2 club Le Havre. Pape Souare was the other Teranga Lions scorer.