Five Oman batsmen were dismissed for ducks as they were skittled in just 17.1 overs, with Khawar Ali striking the only boundary of the innings in his top-score of 15.
Scottish seamers Ruaidhri Smith and Adrian Neill both finished with figures of 4-7.
Oman's highest partnership was just eight runs as they posted the fourth-lowest score in List A history, six runs better than the 18 made by West Indies Under-19s against Barbados in 2007.
Scotland, who narrowly missed out on qualifying for this year's Cricket World Cup, completed their run-chase in just 20 balls as openers Matt Cross and Kyle Coetzer hit four boundaries between them.
"We want to be dominant. We want to be ruthless. And that's exactly what happened on the pitch. We got on top of them and wouldn't let them go," Scotland's acting head coach Toby Bailey told cricketscotland.com.
The sides will play two more games in the three-match series on Wednesday and Friday.