Georgia Stanway’s first half penalty proved the difference, with our City trio all starting at the Brisbane Stadium.
Greenwood featured at left-back for Sarina Wiegman’s side with her set-piece delivery a constant threat, while Kelly and Hemp occupied either flank.
Ellie Roebuck, Esme Morgan and Laura Coombs weren’t called into action on this occasion.
The reigning European champions were heavy favourites ahead of kick-off but were pushed to their limits by the tournament newcomers.
Indeed, Haiti should probably have opened the scoring early on when Roselord Borgella dragged an effort wide of the far post after breaking through.
But England were seemingly presented with a golden opportunity to take the lead before the 20-minute mark when Kelly was brought down in the area, only for a VAR review to spot a foul by Alessia Russo in the build-up.
That sight of goal seemed to settle the Lionesses, with Kelly in particular causing problems out wide.
The winger whipped an inviting ball into the path of Russo once again soon after that penalty shout, with the Arsenal forward clashing with Haiti goalkeeper Kerly Theus as she attempted to get on the end of the cross.
The breakthrough would follow from the spot midway through the first half though, when Batcheba Louis clearly handled the ball inside the area.
Stanway would see her initial spot kick saved by Theus, but an encroachment from the Haiti goalkeeper presented the former City midfielder with another opportunity from 12 yards, which she duly took.
Hemp almost doubled the advantage on the stroke of half-time when her clever diagonal run was spotted by Stanway, but the winger couldn’t make a clean contact from a decent position.
Haiti were far from out of the contest though, and a brilliant ball into the England box almost yielded an equaliser when Borgella glanced a header just wide of the post.
The Lionesses were thankful to Mary Earps early in the second half when she palmed away a stinging long-range drive by the lively Melchie Dumornay.
And her Haitian counterpart made a similarly impressive stop to deny Russo at the other end, when the forward volleyed towards the near post after cleverly turning away from danger.
Hemp made way for Lauren James on the hour, with a grandstand finish beckoning in Brisbane.
Haiti, spearheaded by Dumornay, continued to threaten on the counter, but England were guilty of squandering a gilt-edged opportunity when captain Millie Bright smashed a volley over the bar from inside the box.
The Lionesses’ push for a second intensified when Kelly flashed an effort just wide of the mark having cut in on her left foot, while Greenwood was starting to enjoy greater freedom out wide.
A frantic second half edged towards a thrilling finish, with Earps making a crucial save with her feet when Roseline Eloissaint stole into the box, before substitute Rachel Daly went close at the other end with a header.
Despite that late excitement, England would hold on for all three points, but they were pushed all the way by a Haiti side who, on another day, could have taken something from the game.
The Lionesses are next in action on Friday 28 July when they face Denmark in Sydney.
