In a tournament that has so far been dominated by penalties, it was perhaps unsurprising to see a spot kick awarded at the Brisbane Stadium, as Batcheba Louis was penalised for a handball.
Stanway saw her initial effort saved, but encroachment from Kerly Theus allowed the England midfielder to make amends from the retake.
Alessia Russo led England's search for a second goal after the restart, but she was unable to find a way past the defiant Theus.
While at the other end of the pitch, Mary Earps was forced into action by Melchie Dumonay and Roseline Eloissaint to ensure that the Lionesses begun their World Cup campaign with maximum points.
After being selected ahead of Rachel Daly and Beth England, Arsenal summer signing Russo was presented with the opportunity to grab an early opener, but she could only guide her effort straight at Theus.
Haiti were not prepared to allow England to have it their own way, and they went sent a warning shot when Roselord Borgella raced through on goal before dragging her low strike wide of Earps' goal.
While Haiti showed promise on the counter-attack, their positive start came undone just before the half-hour mark when Louis was penalised for a handball in the box, ensuring that a penalty has been awarded in each of the opening eight games at the tournament.
Stanway's initial spot kick was smartly saved by Theus, but she was given a lifeline after replays showed that the Haitian goalkeeper had moved off her line.
The Bayern Munich player made no mistake at the second time of asking, driving her spot kick low into the bottom corner.
Dumonay led the Haiti response after the break, driving inside from the left flank before drawing a smart save from Earps.
With Haiti posing an obvious threat, England were desperate to find a second goal, but they were resisted by some inspired goalkeeping.
Russo was denied on three occasions by the Haitian shot-stopper, and her replacement Daly experienced similar frustration when her downward header was kept out by Theus.
In the final 10 minutes, Earps was required to stop Eloissaint in a dangerous one-on-one situation, ensuring that England begun their campaign with a narrow win.
The Lionesses will now focus on Friday's meeting with Denmark, while Haiti will be hoping to get off the mark when they face China in Adelaide.