William Porterfield completed his 16th Ireland century as they added 73 runs before declaring on 240-7 to leave the Dutch needing an unlikely 343 to win.
Stephan Myburgh's 85 steadied the Dutch after Wesley Barresi suffered a duck.
A 60-run partnership by Ben Cooper and Peter Borren left the Dutch on 186-4 as played was halted at 18:30 BST.
After a number of rain delays in the contest, Ireland utilised their right to play for another hour after the scheduled finish time of 18:00 BST before captains Porterfield and Borren shook hands.
Resuming on their overnight 167-4, Porterfield batted for just 11 more overs before declaring for the second time in the game.
By then Porterfield had shown all his class in an excellent 108 while Kevin O'Brien had chipped in with a quick-fire 50.
The visitors' unlikely run chase took an early blow as Tim Murtagh trapped Barresi lbw without scoring.
However, a second-wicket partnership of 107 between Myburgh and Dan ter Braak helped ensure that they would leave Dublin with a share of the spoils.
Simi Singh was best with the ball for Ireland in the second innings with 2-19 as unbeaten knocks of 37 and 25 from Cooper and Peter Borren ensured the dogged Dutch earned a deserved draw.
The result moved Ireland to the top of the Intercontinental Cup table but they will need to beat Scotland in November and hope that Afghanistan slip up in the one of the two remaining games to retain the title.

The Suffragette Oak in Kelvingrove Park won a public vote from six trees shortlisted in the Woodland Trust Scotland competition.
It was nominated and championed by Glasgow Women's Library.
The oak will now compete with entries from 15 other countries to decide the 2016 European Tree of the Year.
Wendy Kirk, from Glasgow Women's Library, said she was "thrilled" the Suffragette Oak was chosen as the winner.
She said: "I'm sure that the suffragettes would have been delighted to know that nearly 100 years on the tiny sapling they planted has become the Scottish tree of the year."
Carol Evans, director of the Woodland Trust Scotland, said: "One of the reasons for holding the competition is to uncover the hidden history that many trees represent and to encourage people to value and care for them."

Three open-top buses took the first team, youth team and family members on a parade from Stamford Bridge towards the King's Road in west London.
Chelsea ended their campaign eight points clear at the top after a final day win over Sunderland on Sunday.
The match also marked Didier Drogba's final game for the club after he announced his intention to move on.
Following the championship win, manager Jose Mourinho said: "We have art in our game but we also have fantastic spirit, organisation and pragmatism.
"We are a complete team and that is why we are champions."
The side had topped the Premier League table for a record 274 days ensuring they would be crowned champions for the first time in five years.
Ireland's hopes of retaining the Intercontinental Cup were dealt a blow as they were held to a draw by the Netherlands at Malahide.
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An oak tree planted in Glasgow nearly 100 years ago as a tribute to the city's suffragettes has been named Scotland's Tree of the Year.
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Thousands of football fans turned out to watch Chelsea's victory parade following their Premier League victory.