Graham Potter’s side had a strong grip on Group B4 heading into this clash in Solna, and it became vice-like with two goals inside the opening 11 minutes. Daniel Svensson broke the deadlock when he met Anthony Elanga’s cross with a superb glancing header, netting his first senior international goal in the process.
Their lead was then doubled from the penalty spot after Stjepan Radeljic was penalised for blatantly pulling back Gyokeres in the box, and the Arsenal forward made no mistake in emphatically dispatching the subsequent spot-kick past Martin Zlomislic.
Sweden then appeared to be effectively out of sight when Gyokeres cut the ball back for Alexander Isak with a simple finish at the far post, but the former slightly mistimed his run and VAR spared Bosnia’s blushes.
It had been a bruising first half in more ways than one for the visitors, who were forced into a change when the injured Haris Tabakovic was replaced by Ermin Mahmic. However, there was still time for a further setback before the break when Sead Kolasinac was penalised for a clumsy challenge on Svensson in the box, allowing Gyokeres to net from 12 yards again.
The brace took Gyokeres to six goals in five matches in this Nations League campaign, putting him clear as League B's top scorer, while his total of 27 international goals takes him into Sweden's all-time top 10.
There looked like no way back for the visitors, but they reduced the deficit to two just three minutes after the restart through Armin Gigovic. The Swedish-born midfielder headed home from Mahmic’s cross, providing a glimmer of hope for Sergej Barbarez’s side.
And after Viktor Johansson was twice called into action to keep out Ermedin Demirovic’s header and Kerim Alajbegovic’s driven strike, nerves spread rapidly around the Strawberry Arena as Sweden conceded another goal from a set-piece.
Kolasinac headed home at the near post from Alajbegovic’s corner to score a first senior international goal in his 74th cap, setting up a grandstand finale in the process.
Amar Memic then spurned a golden opportunity to complete a stunning comeback when he fired wide at the far post, and the hosts were indebted to Johansson for a superb one-handed stop to deny Memic again, preserving their slender lead.
Despite a nervy finish, Sweden ultimately held on to secure a 3-2 win and their League A status and extend their unbeaten run into this competition to 12 games, and securing a fourth win in five matches in this group.
Potter’s side have also avoided defeat in each of their previous six games on home soil, and can look forward to facing Europe’s elite sides in the next cycle of this tournament. Another cause for Swedish celebration came at the hour mark, when Dejan Kulusevski was brought on for his first cap in almost two years following his long-term injury.
Meanwhile, it was a frustrating evening for Bosnia, but they will have another chance to secure promotion themselves after cementing second spot and a place in the League A/B play-offs after Poland’s defeat to Romania in the group’s other match.
Review all tonight's UEFA Nations League action on Flashscore.