A Cristiano Ronaldo 4 minute header separated the two sides.
Morocco, playing in its first World Cup in 20 years, linked play neatly through midfield but relied on set pieces for its clearest chances - a growing theme at this year's tournament.
Suarez tapped in midway through the first half after keeper Mohammed Al-Owais failed to grab the ball on a corner.
Ronaldo's 85th global goal made him Europe's all-time leading worldwide goalscorer as he broke Hungary legend Ferens Puskas's 62-year-old record.
Prior to this World Cup, Hungarian forward Ferenc Puskas held the record for the most senior global goals for a European nation with 84 goals between 1945 and 1956.
Sessions says comparing separated children's quarters to Nazi Germany is an "exaggeration"
Still, Trump argued children are being used "by some of the worst criminals on earth" to enter the U.S illegally. Children can't go to jail with their parents, so they're separated.
The result was harsh on Morocco, as was their loss against Iran in their opening game, but it reflected their difficulty producing the telling final ball, despite so much good work in the other two thirds of the pitch.
The Real Madrid forward threatened a second soon after, swivelling on the edge of the area and scuffing just wide after a powerful run from left-back Raphael Guerreiro. Ronaldo will look to close the gap further when Portugal face Iran on Monday.
Though Spain had besieged the Iranian goal in the first half, they were on the back foot for parts of the second, with Karim Ansarifard rifling into the side netting, and Saeid Ezatolahi having a goal ruled out for offside by the Video Assistant Referee (VAR) system.
The most important thing was to win the game and to get the three points.