Ali struck 12 fours and five sixes in his 107-ball strokeful innings and shared 172 runs with Ian Bell (54) for the opening wicket to lay a strong foundation for England after being put to bat at the Hagely Oval.
The 27-year-old Ali hit a six off Majid Haq in the 29th over to score his second career century in his 20th ODI before being dismissed in the 35th over off the same bowler, hitting straight to Freddie Coleman at deep midwicket.
That mini collapse put brakes in the slog overs as England could add 78 runs from the final 10 overs and 48 from the final five.
Captain Eoin Morgan scored a useful 42-ball 46 and shared 49 runs with Jos Buttler (24 of 14 balls) for the fifth wicket to push England for a final assault.
Davey was the most successful Scotland bowler with figures of 4 for 68 in the match which was held four years and one day after the city was rocked by a devastating earthquake which killed 185 people.