Captain Tony Tsabedze struck both goals for a side ranked 117 places below opponents who reached the 2015 quarter-finals in Equatorial Guinea.
Francois Kamano was on target for Guinea, who suffering a second consecutive loss since Luis Fernandez replaced French compatriot Michel Dussuyer as coach.
It was a completely unexpected result in a match moved from Conakry to the Stade Mohammed V in the Moroccan commercial capital because of Ebola epidemic fears.
Swaziland had never won an away Cup of Nations qualifier in 20 previous attempts stretching back to the 1986 eliminators.
But they got precious recent practice in the Cosafa Cup southern Africa championship, defeating Tanzania and Lesotho and drawing with Madagascar.
Guinea were unbeaten in their last seven home qualifiers, including three in Casablanca that helped them qualify for the last tournament.
The west Africans are the top Group L seeds followed by Malawi and Zimbabwe, who meet Saturday in Blantyre, with Swaziland seeded to finish bottom of the mini-league.
Only group winners are guaranteed places in the 2017 tournament to be hosted by Gabon.
Losing to Swaziland coupled with a friendly defeat by minnows Chad in Paris last weekend is sure to pile pressure on Fernandez, who joined Guinea after lengthy negotiations.
Tsabedze, a 30-year-old whose career has included spells with Swazi and South African clubs, broke the deadlock after 11 minutes and scored the winner six minutes from time.
Teenager Kamano,who plays for French Ligue 1 outfit Bastia, scored midway through the second half.
Djibouti are the third worst football team in the world by FIFA rankings, and their weaknesses were brutally exposed in an 8-1 thrashing away to Tunisia.
It took the 2015 Cup of Nations quarter-finalists only nine minutes to break the deadlock at Stade Olympique in Tunis suburb Rades and they led 4-0 by half-time.
Djibouti, ranked 178 places below 2004 African champions Tunisia in the world, reduced the arrears when Mohamed Libane converted an early second-half penalty.
But the Carthage Eagles responded with four more goals to come within one goal of equalling the record winning margin for a Cup of Nations qualifier.
Thrashings are not new for the tiny Horn of Africa state, who conceded nine goals in Kenya and eight in Malawi in previous Cup of Nations qualifying competitions.
Yassine Chikhaoui claimed a 15-minute hat-trick for Tunisia and Ferjani Sassi, Saber Khalifa, Fakhreddine Ben Youssef, Maher Hannachi and Yoann Touzghar were the other scorers.
Togo and Liberia, the other Group A countries, meet Sunday in Lome.
Morocco edged Libya at Stade Adrar in southern Atlantic city Agadir with Omar El-Kaddouri from Italian Serie A club Torino scoring the 51st-minute match-winner
The Moroccans are seeded second and the Libyans third in Group F behind the Cape Verde Islands and ahead of another island state, Sao Tome e Principe.
Another 22 qualifiers are scheduled for Saturday and Sunday while title-holders Ivory Coast have a bye and play a friendly in Gabon.