The first-half display of Herve Renard's men gave every indication they could cause something of an upset in Group B - which also features Spain, Portugal and Iran - as they played some eye-catching football.
While their intensity dropped off in the second period, they are likely to travel to Russia in buoyant mood.
Morocco had little difficulty establishing control and were fully deserving of its early lead, secured by Younes Belhanda in the 11th minute as he converted Ayoub El Kaabi's low cross from close range.
Estonia was its own worst enemy seven minutes before the break, as Amine Harit was clumsily tripped in the penalty area and Hakim Ziyech coolly slotted the spot-kick away.
Proceedings were more even after the interval and Estonia began to offer a threat in the final third, Konstantin Vassiljev testing Munir Mohamedi and Ats Purje shooting just over after a fine solo run.
Purje did get on the scoresheet late on, cleverly making space for himself in the area and finding the bottom-right corner, but just a few minutes earlier Morocco had effectively wrapped things up – Youssef En-Nesyri tapping in Belhanda's pass.
Morocco faces Iran in its World Cup opener.