As Sweden's lead grew, Mexican fans paid more attention to the other game, frantically checking their phones for scoring updates from Germany's game.
Brazil defender Thiago Silva, left, is congratulated on his goal by forward Neymar during their World Cup Group E match against Serbia at the Spartak Stadium in Moscow on Wednesday.
Sweden must win in order to make sure of a second round spot.
But without an improvement on this performance they risk falling once again at the stage where they have been knocked out in the last six World Cups.
That fraught relationship has been transformed into a love affair in Russian Federation, where Mexico stunned 2014 World Cup champion Germany and then dispatched South Korea, 2-1, to close in on a place in the round of 16.
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Despite stunning Italy in the play-offs, not many expected Sweden - without Ibrahimovic - to advance from Group F in Russian Federation.
Berg posed repeated problems for the Mexican defence, his best chance coming when his well-struck shot was acrobatically turned over the bar by goalkeeper Guillermo Ochoa.
Sweden's Sebastian Larsson was booked in the first half for a high challenge on Hirving Lozano and will miss their last-16 match through suspension, as will Mexico's Moreno.
Fabian went close with a shot from distance which deflected just over, but then Mexico imploded as Alvarez bundled the ball into his own net to make it 3-0 to Sweden.
NIZHNY NOVGOROD, Russia - Switzerland is through to a knockout game against Sweden at the World Cup. "We don't need to look at who's not there, we need to look at who will be able to play".
Sweden also had a first-half penalty claim for a handball by Javier Hernandez that was denied despite going to a VAR review, but in the end it mattered little after three second-half goals.
The game had a historic start with Jesus Gallardo collecting the fastest booking since World Cup records began, pulled up after just 13 seconds for a foul on Ola Toivonen. The Swedes stayed crisp in their exchanges and it helped them find seams in El Tri's defence.
Sweden didn't panic despite missing early chances to score.