Ali contributed a masterful 128 runs towards England's total of 303 and Scotland were all out for 184 with more than seven overs remaining.
Although Scotland were outclassed, the win was not as convincing as three-times World Cup runners-up England would have wanted.
After hidings by Australia and New Zealand they were desperate for a confidence-boosting win and the opportunity presented itself against the lowly-ranked Scotland.
But their jubiliation at putting points on the board was tempered by the lack of fight at the back of the innings when they lost six wickets for 102 runs in the final 15 overs.
England had set themselves up for a big total when Ali, supported by 54 from Ian Bell, took them to 201-2 with their 172-run stand for the first wicket the highest opening partnership so far in the tournament.
Ali, dropped in the second over when Freddie Coleman failed to grasp a sharp chance, was untroubled by the occasion as he posted his second career ODI century.
Having been sent in under overcast skies and with swing-friendly conditions at the Hagley Oval, he took a fearless approach to the bowling with a liking for the aerial route to beat the inner field.
His 128 included 12 fours and five sixes while the more sedate Bell only reached the boundary twice in his half century.
Bell had an early life when Alasdair Evans' lbw shout was turned down. Scotland decided not to appeal, although replays showed the ball would have clipped the leg stump.
He was finally undone driving at Richie Berrington to be caught by Kyle Coetzer and Ali followed soon after, undone by the gentle off-spin of Majid Haq.
Ali's dismissal started a run of three wickets in 10 balls for two runs with Gary Ballance (10) and Joe Root (one) removed as England slumped from 201 for one to 203 for four.
James Taylor (17) and Jos Buttler (24) made starts but could not carry on while captain Eoin Morgan added 46 before he was among three wickets to fall in four balls as England pushed to get the score over 300.
Josh Davey, whose first spell only lasted two overs with the first including four wides and the second conceding 14 runs, came back to claim four wickets for an expensive 68 runs.
Facing 304 to win was a huge mountain for Scotland to climb although opener Kyle Coetzer and skipper Preston Mommsen bravely took up the challenge.
A Mommsen boundary took them past the 100 mark in the 22nd over, five overs slower than England but with a healthy seven wickets in hand.
However, the game began to slip from Scotland soon after when Root ended the 60-run partnership for the fourth wicket when he removed Mommsen for 26.
Coetzer, who was dropped by Bell in the first over from James Anderson, was back in the pavillion eight balls after Mommsen for a 71 off 84 deliveries.
From there the last five wickets fell for 62 runs with Steven Finn picking up three for 26.
