Switzerland were the better of both teams in the contest, enjoying a good share of the possession but were unable to break down an organised Wales side in the first half.
But Dragons fought back and equalised in the 74th minute through Kieffer Moore, who also nodded home from a Joe Morrell cross into the box after a short corner routine.
Switzerland had another go at their counterparts scoring in the 86th minute through substitute Mario Gavranovic, but VAR judged him to have strayed offside.
We look at three talking points from the game.
Wales, not a one-man team
In qualifying for the Euros, many people labelled Wales as a team mainly dependent on Gareth Bale, and to a lesser extent Aaron Ramsey.
Despite their run to the semi-finals in 2016 that saw Joe Allen and not the Real Madrid winger or his Juventus counterpart included in the team of the 2016 tournament, the spotlight remained on the more prominent names.
But in Baku on Saturday, the evidence was different as it was the lesser players who dug out Robe Page’s side when they fell behind.
In a toothless first-half showing from Wales, Manchester United’s winger Daniel James was the only bright spark in Wales’ attack as he created two chances and completed one take on.
At the other end of the pitch, goalkeeper Danny Ward was in solid form and was the reason Wales came out of the game with something going into the other fixtures.
Even the equalising goal came from an unlikely combination of Championship players. Striker Kieffer Moore plays for Cardiff City Moore, while Joe Morrell plays for lowly Luton Town.
Teams who hope to stop Wales by stopping Bale and Ramsey will have to rethink their strategy as they prove to be a team not reliant on a single player.
Embolo runs the show for Switzerland
While Wales were accused of being a one-man team, the same was not said of Switzerland.
But on Saturday afternoon, it appeared that Switzerland were the ones dependent on one player—Breel Embolo.
The Borussia Monchengladbach striker was at the heart of everything good that happened in the Swiss team.
He showed good strength and awareness throughout the game, combining well with strike partner Haris Seferovic to keep the Wales backline on their feet.
Also, it was his saved shot that led to the corner from which he scored.
Although players like Shaqiri and the aforementioned Seferovic made important contributions, it was the Swiss number 7 who stole the show and was rewarded man of the match for his display.
The Red Crosses will hope for more of the same from Embolo in their remaining group-stage games.
Group A still open
With Italy setting an early pace in the group with a 3-0 win over Turkey, the result on Saturday means that Group A remains open.
Had either team won, it could have set the direction of the group. But as it stands, chances are still there for any team to qualify for the next round.
It is now a matter of who will perform better in the remaining two group games and perhaps finish second behind Italy, who look like they will easily finish top of this group.
Although Switzerland look like the team that will probably qualify, they face Italy next. And should they lose as is likely, and Wales win against Turkey, it means that the pendulum swings toward The Dragons, who can seal a second-place finish if they can draw with Italy in the last group match.
Whatever happens, it promises to be an intriguing group.