Chasing 256, the Dutchmen seemed to be cruising, with ex-Forfarshire pro Tommy Cooper and the hard-hitting Alexei Kervezee in ominous form.
But their charge was halted by the deadly accurate spin bowling of Clydesdale ace Majid Haq, who snapped up three crucial wickets in quick succession.
He then struck again at the start of his next spell as the visitors threatened to hit back.
Afterwards Granite City-born Durham batsman Coetzer, claimed that the Scots are now finding a potent selection and tactical formula for One Day Internationals. He said: "You can see how quickly a game can turn and we were never out of it.
"All it took was a couple of quick wickets.
"We knew Tom Cooper was going to be a big player for them so we had to restrict him as much as possible.
"When he and Kervezee were batting there was some concern, but we had our plans.
"Based on results from the past 12 months or so you would have said Holland would have been the favourites for this one, but we have a good squad of players who are coming on well.
"We are starting to learn how to do our jobs. We were unfortunate in the Pro40 matches against the English counties earlier in the season, we had some good close games, just without being able to get over the line.
"Things are now coming together - the batsmen are scoring runs and the bowlers are performing to plan."
Coetzer went on: "We have to finish things off in the second game. It is another big day, and we have to keep our skills levels high."
The Scots made 255 for seven off their 50 overs, failing to fully capitalise on the solid foundations built by the top order. Fraser Watts and Coetzer took the tally to 86 before the former departed for 33. Coetzer followed for a fine 64 and Calum MacLeod whacked a brisk 35, perishing with the total on 148.
That was the cue for a flurry of further wickets to fall, with Davey and McCallum each making only six. At 180 for five, the Scots were rocking - but Preston Mommsen, Richie Berrington and skipper Gordon Drummond (20) steadied the ship.
Holland strolled to 119 for two before Haq prompted Kervezee into offering a catch to Josh Davey at short fine leg when one short of his half-century. Then he bowled Michael Swart and Tom de Grooth with successive deliveries.
The pendulum swung back in favour of the Dutchmen when Mudassar Bukhari smashed 41 off only 23 balls but when Neil McCallum pouched him, Haq trapped Tom Heggelman lbw at the start of his second spell and Davey got rid of Pieter Seelaar, the Scots were back in charge with three overs left.
The Netherlands needed 21 but they could only scramble a single off Haq. Davey then killed them off by shattering the stumps of Cooper for 75 with the last ball of the penultimate over.