Hiddink returned to coach the national team for the second time after Louis van Gaal departed to take over at Manchester United following last season's World Cup.
The experienced Dutchman has found the going tough this time around, though, and only an injury-time equaliser from Klaas-Jan Huntelaar rescued a 1-1 draw against Turkey on Saturday.
That left Netherlands third in Euro 2016 qualifying Group A - five points adrift of Iceland, who occupy the second automatic qualification spot.
But PSV star Wijnaldum rubbished any suggestion that Hiddink has lost the dressing room.
"It is nonsense to say that it does not work with the coach," he told Fox Sports. "We stand behind the coach."
The focus now switches to Tuesday's encounter at the Amsterdam Arena with Netherlands having beaten Spain 5-1 in the group stages of the World Cup the last times the two teams met.
Wijnaldum added: "We beat them at the World Cup 5-1. They will want to make amends."
Spain's defeat was part of a dire World Cup defence in Brazil that saw them eliminated before the knockout stages and cast doubt over Vicente del Bosque's future.
He remained as Spain coach and they have made decent, if unspectacular, progress since - a 1-0 victory over Ukraine on Friday taking them to four wins out of five in Group C of European Championship qualification.
Midfielder Isco believes the team are not making the most of the chances they create, but the Real Madrid man feels performances have been of a high standard.
"We might not be scoring many goals in the national team lately, but we generate many chances and it's something than can change from one match to another," he said.
"It's important to show solidarity among team-mates.
"We were happy with the three points [against Ukraine] that was important. But we're here to work and to be more consistent during matches."
Spain, who defeated Netherlands 1-0 to win their only World Cup in South Africa in 2010, may have been hammered by the Dutch the last time the sides met, but versatile left-side player Juan Bernat believes that match will have no bearing.
"There's always a rematch in football," he said. "That's what is so nice about this sport."
