Afghanistan, one of the pre-tournament favourites to qualify, made 255 all out batting first, but MacLeod hammered 23 fours and a six in his blistering 146-ball knock to lead Scotland to victory with 16 deliveries remaining.
"The wicket was difficult to bat on, it wasn't coming good onto the bat," said 19-year-old Khan, the first-ever teenager to skipper a men's international side.
"Later on when the sun came out, it was totally different and it was quite easy to bat on. The toss is really important in these games, but that's not in our hands, there's nothing we can do about that."
The 10 teams in Zimbabwe are fighting it out for only two places alongside the world's top eight ODI sides at next year's World Cup in England and Wales.
A famous Scotland win looked unlikely when 16-year-old Afghan leg-spinner Mujeeb Ur Rahman dismissed openers Matthew Cross and Kyle Coetzer inside the first six overs.
But Richie Berrington joined MacLeod at the crease as the pair put on a 208-run stand to see off Afghanistan and gain a measure of revenge for their narrow defeat by the same opposition at the 2015 World Cup.
"It was an unbelievable effort from him. It's a great start to the tournament but we will take every day as it comes."
- MacLeod targets Khan -
========================
Rising star Khan was attacked by MacLeod and conceded 68 runs from his nine overs.
The leg-spinner finally ended the partnership by trapping Berrington lbw, but by then the game was gone and Afghanistan will have to bounce back against Zimbabwe on Tuesday, with only the top three teams from each group to reach the Super Six stage.
"We needed some wickets in the middle and we didn't do that," added Khan.
Earlier, Afghanistan had recovered from 71-4 to post a challenging total thanks to 92 from all-rounder Mohammad Nabi and the big-hitting Najibullah Zadran's 67.
Elsewhere, Zimbabwe restored some confidence after their 4-1 series defeat by Afghanistan last month by crushing Nepal as both Sikandar Raza and Brendan Taylor hit hundreds.
Wicket-keeper Taylor managed an even 100, but the headlines were grabbed by all-rounder Raza's 66-ball 123 that featured nine maximums.
Nepal battled bravely in reply but never threatened Zimbabwe's massive total of 380-6, as Raza added 3-48 with his off-spin in a virtuoso individual display.
Andy Balbirnie's 68 led the Irish to 268-7, before Tim Murtagh took three wickets as the Netherlands slumped to 149 all out in pursuit of 243 from 41 overs.
The UAE, who gave two-time world champions the West Indies a scare in a warm-up match earlier in the week, had little trouble in brushing aside Papua New Guinea to edge ahead of Ireland at the top of Group A on net run rate.
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