The Netherlands had failed to qualify for the previous European Championships and the 2018 World Cup and began their return to the big stage looking like they were desperate to make up for lost time.
However, they were rescued by PSV defender Denzel Dumfries who headed home his first international goal at the far post with five minutes remaining, having earlier wasted a great chance with the game goalless.
Frank De Boer's side registered seven shots in the opening 15 minutes alone with two of their most experienced players, Mephis Depay and Wijnaldum, running the show.
But a combination of ineffective finishing and goalkeeper Georgiy Buschan meant they were frustrated for 52 minutes before the previously impeccable goalkeeper pushed Dumfries' cross straight out to the former Liverpool midfielder and he calmly passed the ball into the net for his 23rd goal in 76 appearances.
Coincidentally, the new Paris St Germain signing was the last player to score for Holland at a major tournament, 2,528 days ago at the 2014 World Cup.
Weghorst, who had been relatively ineffective, fired home his first international competitive goal seven minutes later but the celebrations in Amsterdam's Johan Cruyff Arena were cut short when West Ham winger Yarmolenko curled home a brilliant effort before Yaremchuk's powerful header levelled up the Group C encounter.
At that point there was the potential for the hosts to implode completely but the 25-year-old Dumfries picked the perfect time to open his Oranje account and make it a memorable return after a seven-year absence.
Such was their dominance De Boer's side should have cruised to victory.
Lyon's former Manchester United forward Depay set the tone with a one-man counter-attack from 15 yards inside his own half with barely two minutes on the clock, forcing the first of a number of saves from Buschan.
With both wing-backs in the 3-5-2 formation pushing on it was no surprise to see the right-sided Dumfries regularly appearing in the final third but there was no excuse for him missing a free header from Depay's cross five minutes before the interval.
It was, merely, a prelude to what turned into an exciting finish in which Ukraine's goalkeeper had played his part, making the save of the match as, wrong-footed, he stuck out a left hand to keep out Wijnaldum's deflected first-half volley.