The points were shared in a rainy Hamilton as Norway failed to convert several opportunities to find their first win of the World Cup.
The Swiss started off the better of the two sides following a late injury to Norway striker Ada Hegerberg just before kick off.
But despite applying some pressure on the Norway back line, Switzerland were unable to create anything of note and Norway began to fight back to get a foothold in the game.
And it was Norway who had the first real chance of the game as a cross from the right hand side found the head of Hegerberg's replacement Haug who forced Thalmann in to a smart save.
Switzerland hit back though with a chance of their own after a lovely flowing passing move which resulted in forward Crnogorcevic blazing her effort over the bar.
Overall, it was a fairly even opening 45 minutes as the game entered half time goalless -
chances few and far between for both sides.
Norway came out firing at the beginning of the second half with Mjelde heading on target form a corner but it was straight down the throat of Thalmann.
Thalmann was then forced into action again as she palmed away a powerful effort from Haug.
Both sides knew the magnitude of the game, knowing that they could not afford to lose, even this early on in the tournament.
The Scandinavians continued to press for a vital three points and Thalmann made an impressive double save to first deny Hansen and then Maanum.
The Swiss struggled to get out of their own half as they tried to cling on for a draw with less than ten minutes to go.
Four minutes of added time was not enough for either team to successfully find a breakthrough and the contest ended goalless - a result that favoured Switzerland more than Norway.
The stalemate means Switzerland stay atop of Group A with four points from two games whilst Norway stay bottom and progression to the knockout stages is now out of their onw hands.
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