The Scots successfully chased down a target of 216, with captain Coetzer's 108-run stand along with Michael Leask's 47 crucial as they ground out victory with 12 balls to spare.
After following up their defeat against the United States on Saturday with a victory over the same opponent the following day, Shane Burger's side have now won two of their three games in Texas as they step up their bid to qualify for the World Cup.
They are currently second in the League 2 table, behind Oman and above the UAE, who they face again on Friday to complete this four-game series.
"We spoke as a group in our scouting meeting about how we would react if we lost the toss on a ground and in conditions that have certainly been favouring batting first," Coetzer told Cricket Scotland.
"That happened, but the bowlers adjusted very well and stuck to their plans, defending one side of the field and attacking from the other and we certainly put the UAE under pressure through certain phases of the game.
"Importantly we took our catches too and we were able to hold them to a lowish total because chasing was always going to be tricky on that surface.
"Chris Sole was the stand-out bowler, he has come in and hit a really decent length in the last couple of games, but all of the bowlers put in a shift, especially into the breeze.
"Then came a fighting effort in the second half to try and get over the line.
"We had to graft away and I rode my luck at times, but on that pitch you really had to commit to your shots if you were going to play them and I am just pleased to help the team get some more points on the board.
"In recent times we have relied a lot on Richie Berrington and George Munsey with the bat, so it was good to see other guys chipping in and Michael Leask came in and did a great job for the team when required.
"His innings provided some impetus when it was required and he has been in great form with bat and ball for a while now.
"It was a character-building day in the heat as we got to our target.
"We have done well to win our last two games and will now look forward to Friday. We want to end the trip on a high."