Germany also set a single-game scoring record for the relatively new competition - this is its fourth edition - by routing Bosnia and Herzegovina 7-0.
Gyokeres took his nation's opening goal in the third minute. After Slovakia's David Hancko levelled in the 19th, the Sporting Lisbon striker set up Aleksander Isak to put Sweden back in front for good in the 31st.
Gyokeres is the joint-leading scorer of the Nations League with five along with Portugal's Cristiano Ronaldo and Slovenia's Benjamin Sesko. He recently upstaged Erling Haaland by scoring a hat-trick as Sporting beat Manchester City 4-1 in the Champions League.
Sweden are trying to earn promotion from League C to League B. Estonia finished 0-0 at Azerbaijan in the same group.
The Netherlands joined Germany as the two teams from League A, Group 3 to advance to the quarter-finals in March.
The Dutch easily won their game in Amsterdam, which was briefly suspended in the first half for the medical evacuation of Hungary assistant coach Adam Szalai. The Hungarian Football Federation said the former player was in "stable" condition after being taken by ambulance to a local hospital.
Wout Weghorst converted a penalty in the 21st and Cody Gapko added a second spot kick in first-half injury time. Denzel Dumfries and Teun Koopmeiners added second-half goals.
Bayer Leverkusen midfielder Florian Wirtz scored twice, including from a superb free kick, to help fuel the Germans' demolition of Bosnia and Herzegovina.
Forward Tim Kleindienst also got his first two international goals, while Jamal Musiala, Kai Havertz and Leroy Sane all added to the lopsided scoreline in Freiburg.
Wales escaped with a scoreless draw from Turkey after the host's top scorer Kerem Akturkoglu missed an 89th-minute penalty. Akturkoglu, who leads Turkey with four goals in the Nations League, sent his spot kick off the post.
Iceland won at Montenegro 2-0 after late goals by Orri Oskarsson and Isak Bergmann. The loss meant Montenegro will be relegated to League C.
A goal by Georges Mikautadze got Georgia a 1-1 draw at home with Ukraine after an own goal by Solomon Kverkvelia put the visitors ahead.
The Czech Republic missed the chance to earn promotion from League B after drawing at Albania 0-0.
In League D, Virgiliu Postolachi scored in injury time to give Moldova a 1-0 win in Andorra.
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