Substitute Soufiane Rahimi slipped in the third with the last kick of the match.
It was tough on Canada, who were the better side in the opening period in front of a crowd of 68,777 as they sought to make more history.
They came into the contest in uncharted territory, having won a World Cup match and then a knockout game for the first time to get to the last 16.
They were clear underdogs and their fans were outnumbered by Morocco supporters at the air-conditioned Houston Stadium.
Yet they looked the more confident at the start, Tani Oluwaseyi turning sharply in the box and forcing Morocco’s Montreal-born goalkeeper Yassine Bounou to save with a stretched-out leg after 10 minutes.
From Canada’s fourth corner of the half, defender Alistair Johnston failed to make the most of a free header. Morocco were rattled.
After 20 minutes Mohamed Ouahbi’s team suffered a big injury blow, Bayern Munich-bound Ismael Saibari — who had scored three times at the tournament — coming off for Rahimi.
Immediately after the drinks break Rahimi had a go optimistically from distance, registering Morocco’s first shot on target with a quarter of the game gone.
There was a flashpoint shortly before half-time when Morocco captain Achraf Hakimi and defender Richie Laryea had a brief shoving match, with both shown yellow cards.
Luc de Fougerolles with the ball against Morocco. Photo / AFP
Referee Michael Oliver booked six players – four from Morocco – in a half high on niggly fouls and low on goal-mouth action.
The build-up to the last World Cup game of seven in Houston, with the United States celebrating its 250th birthday, was the highlight until that point.
Morocco, who beat Canada in the group phase at the 2022 World Cup, came out for the second period transformed.
Five minutes after the restart Hakimi pinged a low free-kick to Ounahi unmarked outside the box and he swept in first time.
Canada goalkeeper Maxime Crepeau had his view blocked by two of his defenders and the ball also went through Rahimi’s legs.
On 82 minutes, Ounahi was the man in the right place again on the breakaway with another right-footed first-time finish, before Rahimi pounced in the 98th minute.
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