Coutinho's curling effort had seen tournament favourites Brazil take a 20th-minute lead, but an impressive Switzerland levelled early in the second period, and that was where the scoring ended in Rostov.
Switzerland had the first opportunity of the match inside the first three minutes, but Blerim Dzemaili - who had been found by Xherdan Shaqiri - could only lift the ball over the Brazilian crossbar from close range.
Switzerland enjoyed themselves in the early exchanges, but Brazil upped the tempo as the first period progressed, with Neymar, Coutinho and Gabriel Jesus all finding space in dangerous positions.
It was Coutinho who broke the deadlock in the 20th minute, when the Barcelona midfielder found space outside the Switzerland box before curling an absolute dream of an effort into the back of the net off the post.
Switzerland continued to enjoy plenty of the ball inside the Brazilian half of the field, but the team in red were finding it difficult to pick the final pass as Thiago Silva and Miranda defended their lines.
Thiago Silva had the chance to double Brazil's lead late in the first period when he met a corner from Neymar, but the centre-back's header missed the crossbar as Coutinho's strike separated the two teams at the break.
Switzerland were level less than five minutes into the second half, however, when Zuber headed a Shaqiri corner into the back of the net from close range.
Coutinho twice had efforts blocked in the period that followed, while Neymar saw a strike deflected into the side-netting as Brazil looked to hit back before the hour mark in Rostov.
Fernandinho replaced Casemiro in Brazil's first change of the match in the 60th minute, and the Manchester City midfielder had a long-range strike deflected just wide of the Switzerland post six minutes later, before Renato Augusto entered the field for the Selecao.
Coutinho sliced one wide of the post 20 minutes from time following excellent work from Neymar once again, before Dzemaili tested the gloves of Brazil goalkeeper Alisson Becker down the other end of the field.
Neymar then headed into the arms of Sommer in the 88th minute, before the Switzerland goalkeeper denied Firmino moments later. Miranda also came close to snatching it late for the Brazilians, with the centre-back's volley falling just wide.
Next up for Brazil is a clash with Costa Rica on Friday afternoon, while Switzerland will take on group leaders Serbia.
BRAZIL (4-3-3): Alisson; Danilo, Thiago, Miranda, Marcelo; Coutinho, Casemiro (Fernandinho 60'), Paulinho (Augusto 67'); Neymar, Jesus (Firmino 79'), Willian
SWITZERLAND (4-4-1-1): Sommer; Lichtsteiner (Lang 87'), Schar, Akanji, Rodriguez; Shaqiri, Behrami (Zakaria 71'), Xhaka, Zuber; Dzemaili; Seferovic (Embolo 80')