Sweden badly needed a goal and five minutes after half-time they deservedly got it, defender Augustinsson popping up from left-back to volley in.
Twelve minutes later it was 3-0 as Alvarez scored a calamitous own goal when he sliced the ball onto his standing leg from six yards and it bounced beyond Ochoa.
Mexico players react at the end of the group F match between Mexico and Sweden, at the 2018 soccer World Cup in the Yekaterinburg Arena in Yekaterinburg, Russia, Wednesday, June 27, 2018.
Sweden coach Janne Andersson said that he took no satisfaction from seeing Germany crash out of the World Cup on Wednesday, as his side surged through top of group F in a thrilling and nail-biting finale.
"I'm incredibly proud of the team, they were so disciplined and they were so loyal".
Hirving Lozano will be the main man in Mexico's line-up once again as they seek to confirm their place in the World Cup knockout rounds. "We've definitely grown since the last match".
Captain Andreas Granqvist admitted that the way some of the Germany staff reacted to Kroos' victor left a sour taste and he hopes his players will channel their frustration in a positive way against the Mexicans.
However, the 55-year-old coach is not taking Mexico lightly, with "El Tri" having already beaten Germany and South Korea.
Sweden, who at half-time were heading home from Russian Federation, scored three times in the second half to deservedly beat a ragged Mexico 3-0 in Yekaterinburg.
Andersson had been upset by Germany's celebrations in a last-gasp 2-1 win for the holders last weekend, but said he took no satisfaction from seeing them crash out. "That match made us stronger, more confident".
The defending champions from Germany go home early.
Sweden were on course for the last 16 until Toni Kroos stepped up with a wonderful victor in the fifth minute of injury time to rescue the reigning champions 2-1 in a Saturday-night thriller.
But the Mexicans also threatened several times to score. "We don't need to look at who's not there, we need to look at who will be able to play".
"I've seen the images, we heard from players and leaders afterwards that the behaviour was very poor on behalf of the Germans", the defender added.