Cape Verde added a third goal in added time when Stopira, a substitute for Joao Paulo, pounced on a loose ball to score.
Cape Verde rely heavily on players born outside the nation to Cape Verdean parents or grandparents. Livramento was born in Rotterdam and Semedo near Paris.
Eswatini had come to the 10-island archipelago with little attacking ambition, adopting a 5-4-1 formation in front of goalkeeper Khanyakwezwe Shabalala.
But after conceding twice, there was no way back for the team from southern Africa, who lost seven qualifiers and drew the other three.
Cape Verde spread the national team net wide with three starters based in Portugal and one each in the United States, Republic of Ireland, UAE, Romania, Russia, Netherlands, Turkey and Cyprus.
The remarkable qualification of Cape Verde came after they made a disappointing start to the 10-match campaign, drawing 0-0 at home with Angola and slumping to a 4-1 loss in Cameroon.
Those results left the Blue Sharks with four points from a possible nine, having won away to Eswatini in between.
But after the matchday three loss in Yaounde, Cape Verde won five consecutive qualifiers, including crucial one-goal victories away to Angola and at home to Cameroon.
That left the islanders needing three points from their final two qualifiers this month and a drama-filled 3-3 in Libya secured one before hosting Eswatini.
Last year, in the midst of the World Cup campaign, Cape Verde fared poorly in 2025 Africa Cup of Nations qualifying, winning only one match of six and failing to secure a place at the tournament.
Despite flopping in a group from which Egypt and Botswana advanced, Cape Verdean officials retained faith in long-serving coach Pedro Leitao Brito.
After two stints as assistant coach of the national team and spells with five local clubs, the coach popularly known as Bubista took charge of Cape Verde in 2020.
The 55-year-old former centre-back, who represented his country 21 times, guided Cape Verde to successive AFCON tournaments, in Cameroon three years ago and Ivory Coast last year.
They reached the knockout phase each time, making a last-16 exit, then losing a quarter-final against South Africa on penalties after having four spot-kicks saved.
In Group H, already-qualified Tunisia achieved a ninth victory by overcoming second-placed Namibia 3-0 near Tunis with Hannibal Mejbri from Premier League outfit Burnley among the scorers.
The Carthage Eagles, who will make a seventh appearance at the World Cup next year, scored 22 goals in 10 qualifiers and did not concede.
Despite the loss, Namibia edged Liberia on goal difference for the runners-up spot, but will finish last in the table for second-placed nations and be eliminated.
Having suspended French coach Nicolas Dupuis after a five-goal hiding from Senegal last Friday, South Sudan kept a clean sheet in a 0-0 Group B draw with fellow eliminated side Togo.
Top spot in the section rests between Senegal, the leaders with 21 points, and the Democratic Republic of Congo, who are two points behind. Both play their final qualifiers tomorrow.
Qualified teams for the 2026 Fifa World Cup
OFC (1)
New Zealand
AFC (6)
Australia, Iran, Japan, Jordan (debut), South Korea, Uzbekistan (debut).
CAF (6)
Algeria, Cape Verde (debut), Egypt, Ghana, Morocco, Tunisia.
CONCACAF (3)
Canada (co-host), Mexico (co-host), United States (co-host).
CONMEBOL (6)
Argentina, Brazil, Colombia, Ecuador, Paraguay, Uruguay