The Dutchman powered home a header to earn The Reds a share of the spoils after they twice fell two goals behind to a side who were reduced to ten men just before half-time.
Substitute Luke Thomas brought the score back to 2-1 shortly after his arrival on the field, but headed goals from Roger Riera and Veldwijk were required to earn Jimmy Gilligan’s men a point after Leeds extended their lead to 3-1.
Speaking to Forest Player after the match, Gilligan said: “The message we are going to be giving to the boys is one about composure. I thought it was all too fretful. We got a goal back but conceded straight away, rather than getting composed and staying together.
“We probably had enough chances to win it, but we concede soft goals and don’t manage the game properly, so we need to look at that.
“It’s a question of having a look at the DVD and seeing how we can do a little bit better when, one, we have an extra man and, two, when we get ourselves back into the game.”
Click here to watch the full interview with Gilligan and match highlights on Forest Player, or read on for a match report.
Veldwijk was the only senior professional in a squad which was missing the likes of Oliver Burke, Tyler Walker and Josh Rees. But despite their youthful line-up Forest started the match well, Edouard Shoenecker, Matty Cash and Veldwijk all having opportunities in the opening 25 minutes.
The visitors were then left frustrated when Riera and Joe Worrall both made excellent defensive interventions, before Whites stopper Eric Grimes made an excellent save to deny Forest forward Nicolay Todorov from close range after a strong run and cut-back from Veldwijk.
Leeds were growing into the game more as the half wore on however, and it was Reds keeper Ross Durrant’s turn to protect his goal when Zac Thompson and Brian Montenegro tested him twice in quick succession.
But, minutes after Veldwijk had headed the ball narrowly wide under pressure, Durrant was beaten by a brilliant overhead kick from Kalvin Phillips.
Forest did their best to respond but Derrick Otim could only fire the ball over the bar on the turn, before Phillips scored another spectacular goal – this time a free-kick which left Durrant helpless.
An eventful first half was capped by the dismissal of Leeds defender Dario Del Fabro, who was red-carded after an off-the-ball clash.
Both sides exchanged half-chances in the opening stages of the second half as Otim and Shoenecker were replaced by Thomas and Ryan Yates.
And Thomas made a speedy impact when he latched on to Veldwijk’s through ball to finish brilliantly past Grimes.
But Forest couldn’t hammer home their advantage, allowing Montenegro the opportunity to loft the ball beautifully over Durrant and into the far corner to make it 3-1.
The game was being played out at a frantic pace as Forest sought a way back into the match, and they found one when Riera headed the ball home from Cash’s corner on 67 minutes.
Leeds were looking resolute, however, and when Todorov, followed by Yates on the rebound, failed to turn the ball home after excellent work from Jack Kelly, the game looked lost.
But there was still time for Veldwijk to play the hero, connecting with a Forest corner at the near post to head his side level in the final minute.
FOREST: Durrant; Kelly, Worrall, Riera (C), Polimos; Cash (MacDonald), Shoenecker (Yates), Crookes, Otim (Thomas); Veldwijk, Todorov.