Despite the lopsided loss, Mexico moved into the round of 16 for the seventh straight time thanks to a second-place finish in the group after wins over Germany and South Korea combined with the Korean victory over the reigning champion.
Second-half goals from defenders Ludwig Augustinsson and Andreas Granqvist, from the penalty spot, plus a comical own goal were reward for a physical display from Sweden, who only made it to Russian Federation by beating Italy in the play-offs.
Mexico's desperate late efforts proved unnecessary, as South Korea gave them a helping hand to the last 16 with their stunning win over Germany.
Sweden, by contrast, look like a side capable of going further - a turnaround for a team that struggled to score in their pre-World Cup games.
With the game fading into injury time and Sweden certain of victory, Mexican fans began to think what was before the game unthinkable - possible elimination.
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Alvarez's own goal was the seventh overall of the tournament, the most in World Cup history, breaking the record of six set in 1998.
Jimmy Durmaz, the winger who was racially abused online after giving away the free-kick that led to Germany's victor, is again on the bench for Sweden. In Osorio's case, it was the first time he hadn't altered his starting 11 in consecutive games since he took over in 2015. Carlos Vela also had a pair of close misses.
Needing only a draw to advance, Mexico started tentatively but somehow reached the break on level terms after surviving a Swedish aerial bombardment and a VAR review when Javier Hernandez appeared to handle the ball in his penalty area.
The Swedes went through to the knockout rounds as the unlikely winners of Group F, taking the beaten Mexicans with them.
Sweden didn't panic despite missing early chances to score. The Swedes stayed crisp in their exchanges on offence and it helped them find seams in El Tri's defence. But its aggressive style also bit them, opening up some counterstrike chances for Sweden, which it took advantage of.