Radja Nainggolan's fine shot after 84 minutes sent Belgium into the knockout stages and a game against Hungary as they finished second in the standings, level on six points with group winners Italy.
The Swedes ended bottom on one point and Ibrahimovic's bold promise that he would never finish with a disappointment proved to be mistaken.
He tried in vain to inspire his team and had a second-half effort ruled out for offside but Belgium, without ever producing their most fluent football, had enough quality to deal with Sweden's sporadic attacks and create opportunities of their own.
"Zlatan has done a lot of important things in his career and would have wanted to go further here," Belgium captain and man-of-the-match Eden Hazard told reporters.
"It was a difficult match, complicated for our defenders. In the first half we had some possession and created chances. Nainggolan scored an important goal and from then on we had to manage the game."
Sweden started brightly and Marcus Berg's fierce snap shot was parried away by Belgium goalkeeper Thibaut Courtois.
Belgium responded with a surging run by mid fielder Kevin de Bruyne that set up Romelu Lukaku for a shot just wide and a mazy dribble across the edge of the area by Hazard ended with a De Bruyne strike on goal.
Ibrahimovic sprung into life with a shot just past the post but it was a rare attacking foray by Sweden who were pushed back deep by the strong-running Belgian midfield.
De Bruyne whipped in two dangerous crosses from the left and from one of them Thomas Meunier flashed a header narrowly wide just before halftime.
Sweden enjoyed a good spell of possession after the interval and Ibrahimovic hooked the ball into the net from close range but the effort was ruled out for offside.
De Bruyne tested goalkeeper Andreas Isaksson with a fierce long-range strike and after Sweden cleared another dangerous cross the ball fell to mid fielder Nainggolan whose rasping 20-metre shot flew into the top corner of the net.
Ibrahimovic threw the ball away in frustration as the Belgian players celebrated and Sweden's talismanic captain cut a forlorn figure after the final whistle as he slowly walked over to applaud his team's yellow-clad fans.
"I’m very disappointed," Sweden coach Erik Hamren said.
"We were talking before the game about the honour of representing Sweden and of being here but I couldn’t have asked for much more from my players. I’m proud of them, even though we lost."
(Editing by Toby Davis)
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