Berrington plundered 107 off 90 balls in an innings which included six sixes and four fours to guide the tourists to a total of 300 for seven from their 50 overs at Moosa Stadium in Pearland, some 20 miles south of Houston.
A day after the Scots lost their opener against the USA by 104 runs, the 35-year-old joined opener Matthew Cross, who was eventually run out for 74, at the crease with the score on 60 for two and he remained there until the end.
He and George Munsey, who made 51, put on 116 for the fourth wicket with Berrington reaching three figures in style with a maximum from the first ball of the final over.
Safyaan Sharif dented the home side's response by removing openers Steven Taylor and Sushant Modani with just 41 on the board, and they were reduced to 99 for three when Dylan Budge ran out skipper Monank Patel for 36 in the 20th over.
Two wickets apiece for Michael Leask and debutant Chris Greaves put paid to hopes of a middle-order fightback, and Chris Sole mopped up the tail to finish with three for 40 with 7.2 overs to spare.
The Scots have now won eight of their last nine one day internationals.
Next up in World Cup League 2, they have back-to-back matches against the United Arab Emirates at the same venue on Tuesday and Friday before returning home.