Brazil had scored 16 goals in their four previous wins against the Saudis but the home side matched the visitors, particularly in midfield, for most of the game.
Brazil had the better of the first half and Jesus finally broke the deadlock just two minutes from halftime when he ran on to an inch-perfect pass from Neymar and slotted the ball home from an angle.
Forward Neymar was again Brazil's best player but his team mates let him down with their finishing as Saudi Arabia came into the match more in the second period.
The hosts could not score, however, and it fell to Sandro to give the scoreline a more realistic look when he headed home Neymar's corner in the sixth minute of stoppage-time.
Brazil also had two efforts disallowed for offside and Saudi keeper Mohammed Al-Owais was sent off five minutes from time after VAR confirmed he handled the ball outside the box.
"We're aware we need to get better, that we can do better," Sandro said. "Obviously the climate was influential, we have new players who need to fit in, but we deserve congratulations."
Brazil's next game is against Argentina in Jeddah on Tuesday.
The Argentines beat Iraq 4-0 on Thursday to extend their unbeaten run since the World Cup to three games.
(Reporting by Andrew Downie, editing by Ed Osmond)
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