He surpassed the previous best of 175 scored by Calum MacLeod in 2014 and now has more than 5,000 runs for Scotland in all formats.
The 32-year-old left-hander looked all set to carry his bat for a double century but was bowled by Vivian Kingma in the 49th over from the 150th ball he faced.
Matthew Cross, filling in for the ill Richie Berrington as captain, pitched in with 59 runs.
There was also a late cameo from Michael Leask, who hit three sixes on his way to an unbeaten 28 from 14 deliveries as Scotland finished on 369-6, their third highest ODI total.
Sharif took his 259th international wicket in all capped matches when he removed Dutch opener Michael Levitt for 44.
The 34-year-old, who made his ODI debut in 2011, then combined with Munsey to reduce the visitors to 75-2.
However, Teja Nidamanuru, with 51, and Noah Croes, with his own half-century, kept the scoreboard ticking until O’Dowd ensured victory with a thumping six with four balls to spare.
It meant the Dutch matched their highest score in an ODI – the 374-9 they achieved in a dramatic World Cup qualifying win against West Indies two years ago.
