With 20 minutes gone, Coutinho gathered a clearance 25 yards from goal and curled a marvellous shot into the far corner off the post to give the five-times world champions the lead.
Switzerland were well-organised throughout and Brazil created chances but failed to convert them as Neymar and his teammates lacked the guile to secure the win, becoming the latest of the tournament favourites to stumble.
Brazil came into the game unbeaten in their last 18 World Cup opening round fixtures but it was the Swiss who settled the quicker of the two sides and made inroads into the their defence in just the third minute off the game.
"I was expecting to get a victory so, of course, I'm not happy with the result", Brazil coach Tite told a news conference.
With World Cup time upon us, Rob Pizzo breaks down what you need to know about one of the biggest events in the world.
Since 1966, Brazil have scored 37 goals from outside the box at the World Cup - 11 more than any other team. "There was a lot of pressure and anxiety on the players and that translated into the finishes that were not precise".
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"We had some good, clean situations but could have been more precise".
In their first World Cup game since famously losing 7-1 to Germany in the semi-final in Rio four years ago, Brazil took their time to warm up.
"I am proud of their determination", Petkovic said of his team. The second play you can interpret but the first one you can't discuss - the people responsible for that must work within fairness.
Instead, Brazil's second most expensive player, Coutinho, pulled the strings, constantly finding right winger Willian and drifting striker Jesus with sweeping passes although Switzerland managed to deal with the threat.
It was Coutinho who stood out for Brazil with his dazzling display.
Brazil always looked in control until they ceded a corner and Zuber took full advantage of their collective lapse of concentration to level.
Meanwhile, Tite's opposite number Vladimir Petkovic said he hoped his team would get some deserved recognition for the hard-earned point after few had given Switzerland a chance against one of the favourites in Russian Federation.
"I'm very glad to score but what was important was our effort to win and what we did as a team is what counts", Coutinho said. "Sometimes there is a lack of recognition (in Switzerland's ability) and I think that's a pity because this team really believes in itself and can achieve results".