Roberto Martinez's side had bounced back in style from their 2018 World Cup semi-final defeat to France – defeating England, Scotland, Iceland and Switzerland – but had to settle for a draw against their neighbours at the King Baudouin Stadium in Brussels.
The hosts had started brightly, taking a fifth-minute lead through Dries Mertens' 16th international goal, but were pegged back in the 27th minute when Groeneveld – making his first start for Ronald Koeman's side – slotted in from close range.
Substitute Michy Batshuayi looked threatening during the second half, but was unable to find a goal that would have extended the Red Devils' winning streak.
Belgium started in ominous fashion and were soon ahead. Donny van de Beek's headed clearance went only as far as Mertens, who cracked a stunning half-volley into Jasper Cillessen's top-left corner from 15 yards.
A stretching Romelu Lukaku headed over from Mertens' cross soon after, while Simon Mignolet thwarted a clean-through Memphis Depay midway through the first half.
Koeman's side then took full advantage of Timothy Castagne's wayward pass, Depay sliding across the face of goal for Groeneveld to slot under Mignolet from eight yards.
Quincy Promes came agonisingly close to handing Koeman's side the lead soon after, but his fizzing left-foot strike from 25 yards crashed back off the post, while Eden Hazard clipped just past the upright as the sides went into the interval level.
Belgium's Batshuayi – who replaced Lukaku at the break – and Youri Tielemans both flashed efforts wide of Cillessen's right-hand post within minutes of the restart.
The closing stages saw Mignolet paw away Nathan Ake's header, before the lively Batshuayi almost won it at the other end late on, only for Cillessen to push away his instinctive effort, ensuring a share of the spoils.
What does it mean: Belgium fade away after electric start
After four wins on the spin and an early goal, it would not have been a surprise to see Belgium punish their visitors even further. Netherlands are rejuvenated, however, and – after a morale-boosting 3-0 win over Germany last week – demonstrated they are made of sterner stuff under Koeman.
Depay delivers for Dutch
The Lyon forward was full of his usual tricks and flicks but had the substance to back up his style. His pass for Groeneveld's leveller was clinical and he was unlucky not to cap his sparkling display with a goal.
Batshuayi blows his chance
Batshuayi looked lively during a second half disrupted by a raft of substitutions, but the Valencia striker will know that the only way to either displace or partner Lukaku in Belgium's first-choice XI is to finish chances when they fall his way.
Both sides return to Nations League action in November. Belgium face Iceland and Switzerland in League A Group 2, while Koeman's side take on World Cup winners France and then Germany in Group 1.