The match began with a fast and frantic energy as both sides pressed but neither nation found the ability to dominate early on, creating a balanced game.
"We have a gameplan and they do not stray from it one millimeter", said Andersson of his team, aside making up for its lack of superstars - notably Zlatan Ibrahimovic, who retired from global football after Euro 2016 - with unity and spirit.
Both have enjoyed their high points in Russian Federation so far - Sweden with that emphatic second half against Mexico, Switzerland in dramatically beating Serbia - but they'll be sincerely hoping they have something left in the tank.
It was an afternoon laced with regret for a Switzerland side that struggled to wear down their disciplined opponents.
"It brings tears to my eyes", Forsberg said, "and makes me so proud".
It seems to wrong to single out an individual when victory was the outcome of a strong team dynamic but central defender and skipper Andreas Granqvist epitomised all that was good about his team.
A small detail from a awful match but indicative of its low quality and indicative of what England will face in the quarter-final of the World Cup this weekend.
But the stalemate continued until the 66 minute when Forsberg's well struck, goal-bound strike deflected off Manuel Akanji (1-0).
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Emotions will no doubt be high again as Sweden, in its 50th World Cup match, achieved back-to-back victories for the first time since hosting the competition in 1958.
This was only Switzerland's fourth defeat in their last 15 matches at the last four World Cup tournaments, with three of those defeats coming by a 1-0 scoreline.
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Switzerland could consider itself unlucky to be eliminated by a deflected shot from Emil Forsberg, but it was also a victim of its own overcautious play - a failure to seize control of a match that their lofty ranking suggested they should have won easily.
With the final action of the first period, Rodriguez crossed from the left and Olsen lost the ball but Sweden scrambled it away.
Overall, though, Switzerland are still a team very much on the up.
"It is wonderful; we don't get that many opportunities". We should have done better but were simply below par and not good enough to win the game.
"I think you'd have to ask everyone else that question".
However, while not the most pleasing side on the eye, Sweden's basic approach with battering ram strikers Ola Toivonen and Marcus Berg in an old-fashioned 4-4-2 set-up has taken Janne Andersson's side past the Netherlands and Italy in qualifying and helped send world champions Germany home at the group stage. We all work so hard for each other on and off the pitch. "We know we are a good team, that we've earned our successes - we know how we got this far", the 55-year-old explained.