Ludwig Augustinsson volleyed in his first international goal from close range to put Sweden ahead five minutes after the interval.
Soon after the hour mark, Sweden defender and captain Andreas Granqvist doubled their lead from the spot to fire in his second penalty of the World Cup.
At the same time, Mexico midfielder Jesus Gallardo picked up the fastest yellow card in the history of World Cup.
Gallardo was booked after charging straight into the back of Swedish striker Ola Toivonen just 13 seconds into the match.
It was the quickest booking since cards were introduced at the 1970 edition of the tournament in Mexico.
READ MORE: Mexico Beats FIFA 2014 Champion Germany 1-0 at FIFA World Cup in Russia
Previously, Mexico toped Group F, which includes defending champions Germany, Sweden and South Korea. The team won both its first matches in the tournament but has never achieved three consecutive victories in a World Cup.
"Over 8,000 [Swedish] fans have arrived here today. It is arguably more than in the entire history of the Russia-Sweden relations," Swedish Ambassador to Russia Peter Ericson, who came to Yekaterinburg for the match said as quoted by the department.
The Sweden-Mexico match was the last World Cup game to be played at the Yekaterinburg Arena.