Sri Lanka, currently the sixth-ranked one-day international side, are warming up for the Champions Trophy and had inflicted a 148-run loss on Scotland when they last met at the 2015 World Cup.
However, openers Coetzer and Cross helped Scotland past Sri Lanka's 287 total to record a first victory over an ICC Full Member team.
Sri Lanka chose to bat and looked to be on course for a strong target as opener Kusal Perera made a near run-a-ball 57 while Dinesh Chandimal top-scored with 79 and Chamara Kapugedera added 71 including six boundaries as well as four over the rope.
Alasdair Evans and Stuart Whittingham took three wickets apiece for the Scots.
Grant Bradburn's side then set about the Sri Lanka attack as Coetzer and Cross swiftly brought up the half-century stand in the 10th over.
The partnership was finally broken with 201 on the board when Coetzer was caught by Sri Lanka captain Angelo Matthews off Thisara Perera for 118, which came off 84 balls and included 15 boundaries as well as four sixes.
Despite Sri Lanka picking up a couple of cheap wickets, Cross continued to drive Scotland on towards their victory target, as he finished unbeaten on 106 from 123 balls.
Scotland captain Con de Lange was 19 not out as his side made 291 for three off 42.5 overs in their memorable victory.
The County Ground at Beckenham in Kent does not hold full one-day international status, but Coetzer believes Scotland should still enjoy the merits of their success in the 50-overs contest.
"It's been a great day. Firstly the sun was shining and we played a great game of cricket, particularly to restrict them to less than 300 which was an outstanding performance," the batsman said on www.cricketscotland.com.
"It was one of those days, if it goes your way you have just got to keep riding that wave.
"Quite often in the past we would have gone into our shell and not felt that we were up to the task, but out there trying to put them on the back-foot most certainly showed we were up for the task.
"I am pleased for the guys out there to get that historic win."
The two teams will meet again on Tuesday.
